LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


AN    INTEODUCTION 


TO   THE 


ELEMENTS  OF  SCIENCE 


ST.    GEORGE   MIVART,    F.R.S. 

%| 

AUTHOR  OF 

"TYPES  OF  ANIMAL  LIKE,"  "ESSAYS  AND  CRITICISMS," 
ETC. 


WITH  ILLUSTRATIONS 


BOSTON 
LITTLE,    BROWN   AND   COMPANY 

1894 


FUED 


TO    THE   DEAR  MEMORY 

OF  MY  FA  THF.R 

JAMES  EDWARD   MIVART, 

U  HO  BY  HIS  TOIL  FREED  ME  FROM  SORDID  CARES 

WHILE  HE  EVER  ENCOURAGED  ME  TO  LOVE 

AND  WORK  FOR  SCIENCE, 

/  DEDICATE 

THIS     LITTLE     BOOK 


216979 


PREFACE 

THAT  a  work  should  be  written  which  might  introduce 
students  to  the  elements  of  all  the  sciences,  has  long 
seemed  to  the  author  of  this  book  a  thing  to  be  desired. 

Having  been  unable  to  find  associates  for  this  purpose, 
he  has  ventured  to  undertake  it  himself. 

Strongly  convinced  that  the  student  ought  to  be 
introduced  to  mental  as  well  as  to  physical  science,  the 
writer  has  been  careful  not  to  omit  the  elements  of 
psychology,  logic,  and  philosophy,  subjects  which  he 
thinks  have  been  far  too  generally  neglected. 

So  far  as  he  knows,  it  is  the  first  work  of  the  kind,  on 
which  account  he  cannot  hope  to  have  altogether  escaped 
errors,  not  only  as  to  matters  of  fact,  but  also  in  the 
mode  of  their  presentation.  He  therefore  asks  the  in- 
dulgence of  the  reader  who  may  deem  any  subject  too 
fully  or  too  scantily  treated  of. 

ORIENTAL  CLUB, 

October  28,  1893. 


CONTENTS 


CHAP.  PAGE 

I.    THE   STAETING-POINT I 

II.   MATHEMATICS 6 

III.  MECHANICS   ....  40 

IV.  PHYSICAL   FOECES          .           .  84 
V.   THE  NON-LIVING  WOELD 137 

VI.   THE   LIVING   WOELD 185 

VII.   MAN 251 

VIII.   LOGIC 282 

IX.   HISTOEY          ....                                           .  '       .  313 

X.   SCIENCE •           .  365 


LIST   OF  ILLUSTRATIONS 


1.  Origin  of  Roman  Numerals 8 

2.  First  Proposition  of  Euclid 35 

3.  Equilibrium  Through  Opposing  Thrusts        ...  42 

4.  Centre  of  Gravity 44 

5.  Simple  Composition  of  Forces      .....  47 

6.  Complex  Composition  of  Forces   .....  48 

7.  Parallel  Forces 5° 

8.  Levers ,  •  51 

9.  The  Pulley .         -52 

10.  The  Inclined  Plane 53 

11.  Angles  of  Incidence  and  Eeflexion        ....  58 

12.  Velocity  of  a  Falling  Body 61 

13.  The  Pendulum 63 

14.  Liquid  Level  Surface ,     .  69 

15.  The  Siphon .         .  80 

1 6.  Relation  of  Force  to  Distance       .....  97 

17.  Reflexion  of  Energy 99 

18.  Reflecting  Mirrors 100 

19.  Action  of  Convex  Surfaces    ......  101 

20.  Action  of  Concave  Surfaces  ......  101 

21.  Refraction 105 

22.  Aerial  Currents 150 

23.  Two  Aspects  of  the  Earth     .         .         .         .        .         .156 

24.  Geological  Strata  .         .        .         .  .        .         .  167 

25.  Triangular  Measurements 177 

26.  Horse-Tail     .         .         .         .         .         .  .         -191 

27.  Tunicate        .........  192 

28.  Animal  Cell 195 


xii  LIST  OF  ILLUSTRATIONS 

PAGE 

29.  Amoeba          .........  198 

30.  Threads  of  Confervas 199 

31.  Protococcus  .........  200 

32.  Volvox 201 

33.  Venus's  Fly-trap 202 

34.  Bracken-fern          ........  203 

35.  Prothallus      .........  205 

36.  Bean  Plant    .........  207 

37.  Diagram  of  Ovule           .         ...         .         .         .  209 

38.  Leaf  of  Bryophyllum 211 

39.  Buttercup      .........  212 

40.  Kadiolarian   .         .         .       '.         .         .         .         .         ,  214 

41.  Infusorian      .         .         .                  .         .         .         .         .  215 

42.  Hydra    .         .         .         .         .         .         .    .*     .         .         .  216 

43.  Diagram  of  Lion's  Eye .         .                 ...        .        .  220 

44.  Section  of  Spinal  Cord  .         .         .         .         .         .         .  226 

45.  The  Eight  Whale 230 

46.  The  Rhinoceros  Viper   .         .         .        .         .         .         .  23 1 

47.  Tadpoles 232,  233 

48.  The  Eft,  Amblystoma    .         .         ...         .         .  234 

49.  Crayfish         .........  235 

50.  The  Snail 236 

51.  The  Cuttlefish        . 237 

52.  Ichthyosaurus 245 

53.  Plant  Mimicry       ........  249 

54.  Logical  Genus  and  Species    .         .         .                 .         .  288 

55.  First  Logical  Figure 298 

56.  Second  Logical  Figure  .......  298 

57.  Third  Logical  Figure 299 

58.  Fourth  Logical  Figure 299 

59.  First  and  Second  Moods  of  First  Figure       ...  300 

60.  Third  and  Fourth  Moods  of  First  Figure       .         .         .  300 

61.  Fallacious  Syllogism 301 

62.  Dominions  and  Dependencies  of  Alexander  .         .        .321 

63.  Mediterranean  Lands  at  Beginning  of  Second  Punic  War  342 

64.  The  Roman  Empire  under  Trajan          .         .        ,        .  349 


ELEMENTS   OF   SCIENCE 

& 

CHAPTER    I 
THE   STAKTING-POINT 

A  LITTLE  before  the  middle  of  the  eighteenth  century 
Buftbn  published  the  first  volume  of  his  Natural  History. 
It  was  a  wonderful  book,  and  one  yet  more  remarkable 
for  the  sagacious  or  ingenious  theories  it  enunciated  with 
respect  to  human  and  animal  existence,  the  past  history 
of  this  planet,  and  phenomena  of  inorganic  matter,  than 
for  the  many  descriptions  and  figures  of  animals  which  it 
contained.  Its  scope  was  so  great  that  while  it  dealt 
with  such  matters  as  the  origin  of  the  world  and  solar 
system,  it  also  furnished  tables  representing  the  pro- 
babilities of  human  life  and  death — tables  which  have 
helped  forwards  that  vast  system  of  life-assurance,  to 
which  such  a  multitude  of  men  and  women  now  owe 
protection  from  calamity. 

Ever  since  Buffon's  time  science  has  advanced,  and  a 
knowledge  of  it  been  diffused  with  greater  and  greater 
rapidity;  a  similar  and  consequent  increase  in  tne 
comforts  and  amenities  of  life  being  the  general  result. 

As  such  resultiog  advantages  have  become  more  and 
more  apparent,  an  increasing  appreciation  of  science 
itself  has  naturally  followed,  while  even  in  the  earliest 

A 


2  ELEMENTS   OF  SCIENCE 

ages  of  human  existence  men  were  compelled  to  acquire 
some  increase  of  knowledge  with  respect  to  the  world 
about  them,  in  order  to  preserve  their  existence  during 
the  almost  incessant  contests  between  succeeding  races 
of  mankind. 

The  great  majority  of  men  still  pursue  knowledge  as 
a  means  to  attain  material  advantages  of  one  kind  or 
another,  but  there  is  a  rapid  increase  in  the  number  of 
those  who  seek  it  for  its  own  sake. 

This  is  not  to  be  wondered  at,  since  the  gratifications 
which  science  affords  its  patient  and  persevering  followers 
are  exceptionally  great.  Unlike  sensuous  pleasures,  they 
leave  no  sting  behind  them  and  produce  no  depressing 
reaction,  but  are  perennial  and  untiring.  Great  is  the 
contrast  between  the  feverish  pursuit  of  gain  or  the 
heartburnings  of  social  competition  and  the  calm  pleasure 
afforded  by  the  intelligent  contemplation  of  Nature 
• — a  pleasure  which  can  persist  unimpaired  amongst  the 
otherwise  deepening  shadows  of  declining  years. 

Nor  are  these  advantages  beyond  the  reach  of  any 
person  of  merely  normal  capacity.  The  difference 
between  science  and  ordinary  knowledge  is  no  difference 
of  kind  but  merely  one  of  degree.  Science  is  nothing 
more  than  plain  reason  and  common  sense  used  in  a 
methodical  manner  and  applied  to  the  examination  of 
various  objects  around  us,  with  as  much  exactness  as 
possible.  No  one,  therefore,  who  enjoys  such  knowledge 
as  he  has,  and  feels  impelled,  through  love  of  it,  to 
acquire  more,  need  feel  in  any  way  discouraged.  He 
already  possesses  the  scientific  spirit,  and  nothing  but  a 
little  patience  and  perseverance  are  needed  for  him, 
sooner  or  later,  to  become  a  true  man  of  science. 

The  object  of  this  little  book  is  to  assist  the  student 
through  the  very  first  steps  which  he  must  take  in 


THE   STARTING-POINT  3 

such  a  pursuit,  and  to  introduce  him  to  the  means  and 
methods  of  acquiring  scientific  knowledge. 

The  ultimate  scope  of  science  is  to  give  its  pursuer  as 
correct  a  knowledge  as  possible  of  the  nature  of  each 
object  studied,  and  the  causes  which  have  made  it  what 
it  is.  There  are,  however,  a  multitude  of  things  as  to 
which  the  beginner  must  at  first  be  content  simply  to 
know  that  they  are;  but  none  the  less  his  aspirations 
should  always  be  to  know  also  the  how  and  why  they  are 
whatever  they  may  happen  to  be. 

It  is,  then,  necessary  for  our  purpose  to  begin  with 
what  is  most  elementary  and  to  suppose  the  student 
destitute  of  any  scientific  knowledge  of  the  multitude  of 
objects  which  on  all  sides  solicit  his  attention.  He  will 
probably  at  first  be  puzzled  how  best  to  begin  his  study 
of  things  so  various,  as  a  simple  illustration  may  serve  to 
show. 

Let  us  imagine  the  would-be  student  of  science  walking 
amongst  some  partially  wooded  chalk  hills  on  a  brilliant 
evening  in  early  summer.  Birds  are  singing  and  insects 
humming  amidst  abundant  wild  flowers.  Through  a 
gap  in  the  hills  he  catches  a  distant  glimpse  of  the  sea, 
with  here  and  there  a  sail  gleaming  in  the  rays  of  the 
setting  sun.  Entering  the  wood  he  follows  the  margin  of 
a  stream  which  has  plainly  worn  a  way  for  itself,  till  he 
comes  upon  a  few  sculptured  fragments  of  a  ruined  abbey 
which  recall  to  him  some  erroneous  notions  that  existed 
when  the  treasures  of  the  Record  Office  were  still  unpub- 
lished. Meanwhile  dark  clouds  have  gathered  in  the 
east,  and  a  brilliant  flash  of  lightning  suddenly  appears 
amongst  them,  and  he  hears  distant  thunder  while  yet 
the  evening  star  shines  calmly  near  the  rapidly  setting 
new  moon  in  the  still  clear  western  sky. 

What  inquiry  can  we  find  which  shall  at  one  and  the 


4  ELEMENTS   OF  SCIENCE 

same  time  equally  relate  to  all  the  phenomena  which 
will  thus  have  affected  the  student's  senses  ?  What  can 
be  common  to  them  all  without  exception  ? 

Its  nature  must  be  wide  indeed,  since  it  must  be 
common  to  things  so  different.  It  must  be  common 
to  animal  life  and  the  life  of  plants,  to  colour,  to  sound 
and  to  motion,  to  the  sea's  waves,  the  action  of  running 
streams,  the  formation  of  rocks  and  hills,  and  the  move- 
ments of  every  breeze ;  to  thunder  and  to  lightning,  to 
earth  and  to  sky,  to  the  sun,  moon,  and  stars,  to  human 
history,  the  progress  and  decay  of  institutions,  the 
development  of  art,  and  even  to  the  very  thoughts 
which  deal  with  things  so  various. 

Such  a  combination  may  well  at  first  seem  utterly 
bewildering,  and  yet  a  few  very  simple  reflections  may 
serve  to  solve  the  puzzle. 

To  know  anything  whatever,  is  to  know  that  it  is 
distinct  from  something  else.  Two  marbles,  alike  in 
colour  and  size,  shape  and  weight,  are  known  with 
perfect  certainty  to  be  distinct,  though  we  may  not  be 
able  to  tell  one  from  the  other.  We  recognise  them  as 
two  things  of  the  same  kind.  Together  they  form  a 
small  group  composed  of  two  objects.  If  now  these  be 
held  in  the  right  hand,  while  a  third  marble,  exactly  like 
the  other  two,  is  held  in  the  left  hand,  then  the  contents 
of  the  right  hand  differs  from  that  of  the  left  simply  by 
being  "  two  "  instead  of  "  one  " — that  is,  by  a  difference 
of  number. 

But  "number"  is  a  property  possessed  by  all  the 
things  above  referred  to,  since  even  thoughts,  no  less 
than  marbles,  differ  from  each  other  numerically.  Enu- 
meration—  accurate  enumeration  —  is  necessary  for  all 
kinds  of  knowledge.  We  may  feel  things  to  be  hotter  or 
colder,  but  if  we  would  be  accurate  we  must  employ  a 


THE   STARTING-POINT  5 

thermometer  and  note  the  degrees  registered  by  it — that 
is,  we  must  count.  We  see  plainly  enough  that  some 
things  are  bigger  than  others,  but  if  we  would  be 
correct  we  must  measure  them  by  some  standard,  and 
this  again  implies  counting.  It  is  the  same  with 
respect  to  weight  and  motion,  with  respect  to  our  own 
past  history  and  the  past  history  of  mankind.  In  matters 
of  antiquarian  knowledge,  bygone  periods  of  time  have 
to  be  carefully  computed,  and  sometimes  the  duration 
of  nations  and  of  dynasties.  The  velocity  of  winds  and 
waves,  the  rapidity  of  the  lightning's  flash,  as  well  as 
the  seemingly  slow  revolutions  and  displacements  of 
the  heavenly  bodies,  have  all  to  be  also  estimated  by 
counting — that  is,  by  number. 

Thus  the  one  thing  which  alike  pertains  to  everything 
we  know,  terrestrial  or  celestial,  material  or  mental, 
is  "  number."  It  is  a  certain  numerical  relation,  or 
rather  various  numerical  relations,  since,  for  example,  a 
nation  is  one  when  compared  with  other  nations,  but 
multitudinous  when  considered  with  respect  to  the 
individuals  that  compose  it.  This  truth  doubtless  under- 
lay the  system  of  Pythagoras,  who,  five  hundred  years 
and  more  before  our  era,  taught  that  number  was  the 
principle  of  all  things. 

But  the  study  of  that  which  is  thus  common  to  all 
things,  is  the  study  of  mathematics ;  and  therefore 
mathematics,  or  the  science  of  number,  is  and  must  be 
the  most  fundamental  of  all  sciences,  since  it  pertains 
to  every  other,  and  no  other  can  be  pursued  without  it. 
An  introduction  to  the  elements  of  science  must  there- 
fore begin  with  an  introduction  to  the  elements  and 
principles  of  mathematics, 


CHAPTER  II 
MATHEMATICS 

A  STUDY  of  the  first  elements  and  simplest  possible 
principles  of  mathematics,  is  then  what  should  first 
occupy  the  attention  of  every  would-be  student  of 
science.  This  is  absolutely  indispensable,  since  without  it 
no  other  science  is  possible  ;  because  all  of  them,  without 
exception,  suppose  a  greater  or  less  acquaintance  with  it. 

An  objection,  however,  has  sometimes  been  thus 
stated.  It  has  been  said  that  mathematics  is  a  most 
abstract  science,  and  one,  therefore,  unfitted  to  occupy 
the  attention  of  those  whose  object  is  to  gain  a  know- 
ledge of  all  the  concrete,  material  things  about  them — 
the  things  which  they  can  see,  feel,  and  handle. 

Now  it  is  true  that  the  science  of  mathematics  is 
mainly,  and  in  its  simplest  branches  exclusively,  devoted 
to  the  study  of  real  or  possible  numerical  relations, 
apart  from  the  things  which  bear  those  relations. 
Nevertheless  common  sense  shows  us  at  once  that 
numerical  relations,  or  "numbers,"  can  no  more  exist 
apart  from  something  which  has  number,  than  "weight" 
can  exist  apart  from  something  heavy,  or  "dimension" 
exist  without  something  or  other  of  a  definite  size. 
Numbers,  apart  from  real  substantial  things,  only  exist 
as  thoughts,  or  as  the  written  or  spoken  signs  by  which 
we  express  numerical  relations.  But  since  "  numerical 
relations "  have  no  substantial  existence  apart  from 


MATHEMATICS  7 

things  related,  it  follows  that  the  science  of  mathematics 
— which  employs  them — ultimately  concerns  real  sub- 
stantial things  themselves,  to  the  study  of  one  aspect  of 
which  it  is  above  all  devoted. 

Everything  has  number.  Larger  and  smaller  groups 
of  similar  things  differ  in  number,  and  we  can  readily 
express  these  differences  by  spoken  or  graphic  signs  to  a 
certain  extent.  But  the  limitation  of  our  faculties 
makes  it  impossible  for  us  to  think  or  speak  of  a  very 
extensive  series  of  numbers  by  entirely  distinct  symbols. 
Merely  spoken  signs  we  may  at  once  put  on  one  side,  as 
they  are  entirely  devoid  of  the  permanence  requisite  to 
enable  them  to  serve  for  scientific  purposes.  The  art 
of  expressing  numbers  by  means  of  written  signs  is 
called  notation. 

Through  the  eye,  many  such  numerical  symbols 
are  very  readily  recognisable.  Such  is,  for  example, 
the  case  with  the  numerical  symbols  depicted  on  dice 
or  cards,  and  it  is  conceivable  that  specially  gifted 
individuals  might  be  able  to  distinguish  and  recollect 
several  hundreds  of  such  absolutely  different  and  dis- 
tinct numerical  symbols.  That  however  would,  after 
all,  be  of  but  little  utility  for  the  study  of  very  high 
numbers,  wherein  the  most  gifted  imaginations  would 
soon  be  reduced  to  adopt  the  method  employed  by 
ordinary  persons.  .  The  method  usually  adopted  consists 
in  dealing  with  numbers  in  groups,  and  groups  of 
groups,  and  groups  of  groups  of  groups,  and  so  on, 
according  to  some  regular  system,  which  for  one  reason 
or  another  has  come  to  be  the  one  adopted. 

In  the  four  fingers  and  thumb  of  each  hand,  and  the 
five  toes  of  each  foot,  man  possesses  an  easy  and  ready 
means  of  incipient  enumeration,  and  the  words  used  by 
various  savage  tribes  to  denote  numbers,  plainly  show 


8 


ELEMENTS   OF   SCIENCE 


that  this  naturally  suggested  method  has  been  actually 
employed  by  them.  Thus,  the  number  "  five  "  is  some- 
times called  a  "  hand,"  and  "  six"  is  spoken  of  as  "  take 
the  thumb  " — that  is,  "  begin  to  make  use  of  the  other 
hand."  "Twenty,"  the  number  of  all  the  digits  com- 
bined, is  sometimes  denoted  by  the  term  "  a  man,"  and 
"ten  "by  "half  a  man." 

The  same  thing  is  shown  by  Roman  numerals,  where 
I,  II,  III,  and  IIII  indicate  one  to  four  fingers,  while 
"  five  "  is  expressed  by  a  sign  representing  the  thumb 
upstanding  by  itself,  and  the  four  fingers  in  a  group 

FIG.  i. 


V 


opposite  it — V.  To  express  ten,  there  were  the  two 
hands  crossed  obliquely — X. 

Thus  an  arrangement  of  numbers  in  groups  of  ten 
naturally  suggested  itself ;  and  thus  ten  is  the  "  root " 
number,  or  "  radix,"  of  the  system  of  counting  actually 
adopted.  As  written  down  they  form  a  system  of 
notation,  and  there  being  ten  symbols  (0123456 
7  8  9)  to  that  system,  it  is  called  a  decimal  system  of 
notation.  But  other  "  root  numbers  "  might  have  been 
selected,  as  we  shall  shortly  see,  each  giving  rise  to  its 
own  "  system  of  notation." 

The .  Roman    numerals,    though    plainly    expressing 


MATHEMATICS  9 

numbers,  were  found  comparatively  useless  for  purposes 
of  calculation — purposes  which  the  Arabic  symbols  have 
admirably  subserved.  The  absence  of  numbers  being 
expressed  by  o,  and  the  first  group  of  ten  (from  zero  to 
nine)  being  expressed  by  the  figures  with  which  we  are 
all  familiar,  its  completion  is  represented  by  10  (or 
unity  and  zero  combined),  and  so  on  with  successive 
groups  of  ten  till  the  tenth  set  (90-99)  is  completed. 

Then  a  third  figure  is  added  to  the  left  to  denote  ten 
groups  of  ten  (100),  while  each  time  such  a  group  is 
further  taken  ten  times  over,  it  is  expressed  by  the 
addition  of  another  zero  to  the  right,  and  it  is  thus  that 
"  ten  times,  ten  times,  ten  times,  ten  times,  ten  times, 
ten "  (or  one  million)  requires  to  be  denoted  by  the 
figures  1,000,000.  In  this  way  each  figure  shows  its 
value  by  the  place  it  occupies.  Thus  it  is  that  in  the 
symbol  1652392  the  figure  2  denotes  mere  units,  9  the 
groups  of  ten,  3  the  groups  of  ten  times  ten,  or  hundreds, 
and  so  on — or,  in  other  words,  the  symbol  denotes 

1  million,  6  hundreds  of  thousands,  5  tens  of  thousands, 

2  thousands,  3  hundreds,  9  tens,  and  2  units. 

These  truths  are,  of  course,  familiar  to  all  readers  of 
this  book,  though  they  may  not  happen  to  have  con- 
sidered them  from  the  present  point  of  view. 

But  since  our  purpose  is  to  introduce  the  reader  to 
the  elements  of  science,  we  are  bound  to  act  as  if  ex- 
ceedingly little  were  known  by  him.  Thus,  to  carry  out 
the  end  we  have  set  before  us,  we  must  consider  the 
principles  of  such  elementary  processes  as  addition, 
subtraction,  multiplication,  and  division. 

The  definite  position  of  figures,  according  to  their 
value,  greatly  facilitates  the  first  of  these  processes, 
since  by  the  superposition  of  figures,  thus  arranged,  we 
are  enabled  to  add  them  together  as  simple  units,  without 


io  ELEMENTS   OF   SCIENCE 

taking  account  of  the  whole  quantities,  whereof  such 
figures  form  part.  Thus,  in  adding  together  the  quan- 
tities expressed  by  104,  92,  and  8,  according  to  this 
mode,  we  need  take  no  heed  of  the  three  whole  numbers 
as  whole  numbers,  but  simply  add  together  their  super- 
imposed constituent  parts : 

8 

92 
104 

204 

The  result  of  the  above  simple  sum  in  addition  takes 
the  form  it  does,  because  as  the  three  superimposed  units 
at  the  right  hand  together  make  14,  we  know  that  the 
number  of  simple  units  is  4,  together  with  one  group  of 
ten.  When  this  one  group  is  added  to  the  two  super- 
imposed figures  which  form  the  second  column,  the 
product  (because  one  of  them  is  a  zero)  is  ten  groups 
of  ten.  But  a  symbol  of  that  value  cannot  be  written 
down  in  the  second  place,  but  must  appear  in  the  third, 
which  is  that  set  apart  for  groups  of  ten  times  ten.  It 
is  therefore  carried  to  the  third  column,  which  consists 
of  but  a  single  figure  i,  and,  being  added  thereto, 
makes  with  it  two  groups  of  ten  times  ten,  or  200,  so 
that  the  result  must  be  204. 

That  the  results  obtained  by  thus  working  with  mere 
symbols  of  abstractions  applicable  to  all  things  which 
can  be  counted,  accurately  correspond  with  real  rela- 
tions which  exist  between  substantial  things,  is,  of 
course,  most  easily  proved.  For  instance,  if  we  take 
three  parcels  of  things  —  e.g.,  marbles  —  one  of  104, 
another  of  92,  and  the  third  of  8,  and  mix  them 
together,  then  if  we  count  the  whole,  thus  mixed,  we 
shall  find  their  number  to  be  204. 


MATHEMATICS  n 

The  same  system  serves  equally  well  for  subtraction. 
Thus,  if  from  a  group  of  204  objects,  20  have  to  be  taken 
away,  we  write 

204 

20 

Here  it  is  evident  (since  there  is  a  zero  at  the  right  end 
of  the  lower  number)  that  no  single  unit  has  to  be 
taken  away  from  204,  so  the  figure  4  must  remain 
unchanged  at  the  right  hand  of  the  sum  expressing  the 
result.  In  the  second  column  (which  denotes  groups 
of  10)  two  such  have  to  be  taken  from  zero.  This 
difficulty,  as  schoolboys  know,  is  evaded  by  borrowing 
ten  groups  of  ten  from  the  set  of  the  next  higher 
denomination,  then  taking  two  sets  of  ten  from  the  ten 
sets  thus  borrowed,  there  will  remain  8  sets  of  ten,  and 
8  will  therefore  be  the  second  figure  of  the  sum  denoting 
the  result.  The  ten  groups  of  ten,  which  have  been  bor- 
rowed, have  now  to  be  taken  away  from  the  third  figure, 
which  from  its  position  shows  that  it  denotes  groups  of 
ten  times  ten.  This  third  figure  is  2,  from  which  one 
being  deducted,  we  have,  of  course,  i  as  a  remainder, 
and  so  we  express  the  process  thus  : 

204 

20 
184 

The  correspondence  of  this  process  with  the  real 
relations  which  exist  between  substantial  things,  can 
again  be  most  simply  shown  by  taking  20  marbles  from 
204,  and  counting  the  number  left.  In  an  analogous 
manner  we  can  (by  practical,  material  tests)  establish 
the  correspondence  with  reality  of  the  other  processes  of 


12  ELEMENTS   OF   SCIENCE 

the  science  of  number,  which  science  is  the  arithmetical 
part  of  the  great  science  of  mathematics. 

Thus  by  these  arithmetical  symbols  we  can  elucidate 
most  important  results  as  to  real  things,  without  paying 
attention  to  anything  more  than  the  symbols  themselves, 
till  the  result  sought  is  attained.  If  we  know  that  the 
numbers  used  refer  to  marbles  or  any  other  set  of  things, 
we  can  freely  use  them  and  work  out  results  without 
thinking  of  the  objects  to  which  they  refer  till  the  end 
of  the  process.  This  is  of  enormous  assistance  and  a 
prodigious  economy  of  human  effort. 

There  is  no  special  difference  between  multiplication 
and  addition.  Multiplication  is  the  addition  of  any 
number  to  itself  a  certain  number  of  times  over,  and  a 
number  is  said  to  be  multiplied  by  that  number  which 
expresses  how  many  times  the  former  number  has  to  be 
added  to  itself.  Thus  if  10  be  multiplied  by  2,  it  has 
to  be  added  to  itself  (or  taken)  twice ;  if  it  is  multi- 
plied by  9,  it  has  to  be  taken  nine  times,  and  so 
becomes  90.  Nevertheless  though  multiplication  is 
essentially  but  a  form  or  mode  of  addition,  practically  it 
is  a  very  different  process,  and  it  is  one  by  which  we 
can  most  clearly  see  the  great  convenience  of  the  system 
of  numeration  adopted,  and  of  the  practice  of  placing 
figures  in  such  a  way  that  they  express  their  value  by 
their  mere  position. 

The  results  of  a  definite  small  number  of  additions  of 
a  few  small  numbers  have  been  calculated  for  committal 
to  memory  according  to  what  we  know  as  the  multiplica- 
tion table.  This  being  learnt,  two  sums,  the  figures  of 
which  have  been  superimposed  in  due  order  of  value,  can 
be  multiplied  together,  by  the  process  of  multiplying  the 
separate  figures  which  compose  such  two  sums,  just 
as  we  have  seen  that  two  sums  can  be  added  together 


MATHEMATICS  13 

by  the  addition  of  the  separate  figures  which  compose 
them. 

Let  us  suppose  that  the  number  2063  has  to  be  multi- 
plied 345  times;  that  means,  either  that  the  number 
2063  has  to  be  added  to  itself  345  times,  or  that  the 
number  345  has  to  be  added  to  itself  2063  times,  the 
result  of  either  process  being  of  course  the  same.  This 
tedious  process  of  addition  is  avoided  by  the  device  of 
multiplication : 

Thus  2063 
multiplied  by    345 


produces  711735 

In  this  way  we  quickly  arrive  at  the  result  of  adding 
2063  together,  first  5  times,  then  40  times,  and  lastly  300 
times.  If  we  wish  to  test  the  first  process,  we  must  see 
that  2063  added  together  five  times  produces  the  same 
result  as  the  multiplication  of  that  sum  by  the  number 
5,  thus : 

2063 

2063 

2063 

2063 

2063 

10315 

In  obtaining  the  same  result  by  multiplying,  we  see 
by  the  multiplication  table  just  referred  to,  that  5 
times  3  are  15.  We  therefore  set  5  down  at  the 


14  ELEMENTS    OF  SCIENCE 

extreme  right,  but  reserve  the  single  group  of  10  (out  of 
the  15)  till  we  see  how  many  groups  of  10  will  be 
produced  by  the  next  step  of  multiplication.  Our  table 
tells  us  again  that  5  times  6  are  30,  and  the  6  there 
multiplied  (since  it  stands  in  the  second  place  from  the 
right)  denotes  6  groups  of  10,  so  that  30  resulting  from 
its  multiplication  by  5  means  30  groups  of  ten,  to  which 
we  add  the  one  group  of  ten  reserved  out  of  the  15  units 
— making  31.  Of  this  31  we  again  write  down  i, 
reserving  the  3  to  be  added  to  the  sum  of  next 
higher  value.  But  the  figure  which  stands  next  is  a 
cypher  or  zero,  and  5  times  nothing  is,  of  course,  nothing, 
so  all  we  have  next  to  set  down  is  the  3  we  previously 
held  in  reserve.  Lastly  comes  the  fourth  figure  2 
(denoting  two  groups,  each  of  ten  times  ten  times  ten), 
and  this,  when  multiplied  by  5,  becomes  10,  and  so  we 
arrive  at  the  result,  "  ten  thousand  three  hundred  and 
fifteen,"  which  sum  we  also  obtained  by  simple  addition. 
Then  comes  the  addition  of  2063  to  itself  40  times,  which 
is  effected  by  multiplying  the  2063  by  a  4  which  stands 
in  the  second  place,  and  therefore  denotes  not  four  units 
but  4  groups  of  ten.  We  thus  learn  by  a  brief  process 
that  2063  added  to  itself  forty  times  over  conies  to 
82,520.  The  zero  is  not  indeed  written  down  in  the 
process  because  we  have  now  nothing  to  do  with  mere 
units,  the  4  used  in  multiplying  denoting,  as  before  said, 
only  groups  of  ten. 

Similarly  we  can  quickly  see  the  result  of  adding  2063 
to  itself  300  times  by  multiplying  the  former  sum  by  a 
figure  3  standing  in  the  third  place,  which  is  that  set 
apart  for  denoting  what  the  number  of  hundreds  may  be. 
We  thus  see  that  the  addition  of  this  sum  to  itself  300 
times,  amounts  to  the  number  618,900.  The  two  cyphers 
are  not  written  down  because  the  multiplying  figure 


MATHEMATICS  15 

being  one  of  hundreds,  we  have  no  longer  anything  to  do 
with  sets  of  ten  only,  and  still  less  with  mere  units. 
Having  now  these  three  products  of  the  addition  of  2063 
to  itself  5  times,  40  times,  300  times,  we  have  but  to 
place  them  one  under  the  other  and  add  them  up 
thus : 


7H735 

And  thus  we  know  that  the  result  of  the  addition  is 
equivalent  to  the  adding  2063  to  itself  345  times. 

When  a  number  is  multiplied  (added  to  itself)  its  own 
number  of  times,  as,  e.g.,  5,  five  times,  or  9,  nine  times,  or 
1000,  a  thousand  times,  the  product  is  called  the  square 
of  each  such  number.  The  number  which,  by  so  multi- 
plying itself,  makes  that  product,  is  called  the  square 
root  of  that  same  product  whatever  it  may  be. 

When  the  square  of  a  number  is  again  multiplied  by 
that  number,  the  product  is  called  a  cube,  and  the  original 
number  is  the  cube  root  of  such  product. 

The  square,  or  the  cube,  of  a  number  may  be  represented 
by  a  small  figure,  which  is  called  an  index,  placed  on  one 
side  above  the  number  squared  or  cubed.  Thus  the 
indices  2  and  3  thus  placed  with  respect  to  4,  will  be  42 
and  43;  and  these  two  symbols  respectively  indicate  4 
squared  and  4  cubed — which  are,  of  course,  16  and  64. 
The  symbols  J  and  J/  indicate  respectively  the  square  and 
cube  roots  of  any  numbers,  and  thus  ^16  is  4  and  the  ^64 
is  also  4. 

The  number  of  times  any  quantity  is  thus  multiplied 
by  itself  is  called  its  "  power."  Thus  27,  or  2  raised  to 


16  ELEMENTS   OF  SCIENCE 

the  seventh  power,  is  128,  and,  of  course,  any  number 
may  be  raised  to  any  power. 

The  process  of  Division  is  a  form  of  subtraction,  as 
the  process  of  multiplication  is  a  form  of  addition.  It  is 
a  process  which  shows  us,  by  the  aid  of  the  multiplication 
table,  how  many  times  one  number  may  be  contained  in 
another.  Thus,  e.g.,  we  see  that  2  is  contained  8  times 
in  1 6,  because  twice  8  are  16.  We  express  it  familiarly 
thus : 

2)16 


But  the  same  result  is  arrived  at  (and  its  correctness,  if 
need  be,  proved)  simply  by  a  repetition  of  the  process  of 
subtraction,  thus : 

16 

2 


14 

2 

12 

2 

10 
2 

8 

2 

6 

2 

4 

2 


MATHEMATICS  17 

which  demonstrates   that   it   consists  of  2  eight  times 
taken. 

In  dividing  large  numbers  by  one  another,  we  make 
use  of  a  device  analogous  to  that  of  multiplication, 
beginning,  however,  with  the  other  end  of  the  series. 
We  begin  in  this  way,  because,  in  division,  we  have  first 
to  do  with  symbols  expressing  the  highest  value  concerned, 
the  simple  units  coming  last. 

Thus  if,  e.g.,  40,925  be  divided  by  362,  we  then  see  both 
how  many  times  the  lesser  number  is  contained  in 
the  greater  and  what  still  lesser  number  remains  as  a 
residue,  Making  use  of  the  multiplication  table  and 
writing  down  the  process  in  the  usual  way,  we  have  : 

362)40925(113 
362 


472 
362 

1105 

1086 


which  shows  us  that  the  lesser  number  is  contained  113 
times  in  the  greater  number  and  that  19  units  remain 
over. 

As  most  readers  of  this  book  of  course  know,  there 
are  symbols,  not  only  for  numbers  representing  units, 
but  also  for  parts  of  units  or  fractions :  such  as  -J  (a 
half),  J  (a  fifth),  -£  (seven-ninths),  &c. 

The  figure  below  the  line  is  called  the  denominator, 
because  it  indicates  what  proportion  (or  "  denomina- 
tion ")  of  a  whole  number  it  is  ;  while  the  figure  above 
the  line  is  called  the  numerator,  because  it  indicates  of 

v 


i8  ELEMENTS   OF   SCIENCE 

how  many  units  of  that  "  denomination  "  the  fraction  in 
question  consists. 

Here  the  root  number  10  comes  again  into  play  in  a 
way  analogous  to  that  before  mentioned. 

A  tenth  part  being  written  -f^  ,  the  tenth  part  of  a 
tenth  part,  is  expressed  by  adding  a  zero  to  the  right, 
yj-g-,  and  so  on  indefinitely. 

This  fact  has  suggested  a  further  development  of  the 
system  previously  described. 

"We  saw  that  in  any  series  of  figures  expressing  a 
number,  the  figure  at  its  right  extremity  signifies  units, 
while  each  succeeding  figure  to  the  left  expresses  a 
higher  power  of  ten.  Now  evidently  we  may  also  add 
figures  to  the  right  of  the  figure  expressing  units,  and 
then  each  succeeding  figure  will  express  a  decreasing 
power  of  ten,  just  as  well  as  a  fraction  will,  and  we 
place  a  point  to  indicate  the  spot  where  this  decrease 
begins.  Thus  one  and  one-tenth,  which  we  may  write 
as  ij1^,  may  be  equally  expressed  by  i.i,  and  similarly  : 

o~o  by  i.ooi,  and  so  on. 


Thus  892.35  means,  8  groups  of  ten  times  ten  units, 
9  groups  of  ten  units,  2  units,  3  groups  of  tenths 
of  units,  and  5  groups  of  hundredths  of  units. 

So  far  we  have  dealt  only  with  enumeration  according 
to  the  radix  10  —  the  decimal  system  of  notation.  But,  as 
before  said,  the  employment  of  this  radix  simply  arose 
from  the  number  of  our  fingers  and  toes.  "We  may  take 
any  number  as  a  radix,  but  if  we  had  had  six  digits  on 
each  hand,  the  radix  we  should  have  taken  would  no 
doubt  have  been  12,  which  would  have  constituted 
a  duodecimal  system  of  notation.  This  would  have 


MATHEMATICS  19 

been  a  more  convenient  one,  since  12  can  be  divided 
by  2,  3,  4,  and  6,  while  ten  can  only  be  divided  by  2 
and  5. 

To  express  numbers  duodecimally,  i.e.,  when  twelve  is 
taken  as  the  radix,  we  require  two  more  symbols  to 
express  10  and  n  respectively  by  single  figures.  If  we 
represent  10  by  the  symbol  £,  and  n  by  o,  then,  of 
course,  groups  of  twelve  will  need  to  be  represented  by 
two  figures,  and  groups  of  twelve  times  twelve  by  three 
figures  —  groups  of  twelve  always  taking  the  place  of  the 
groups  of  ten  in  the  ten  radix  system.  They  may  be 
expressed  as  follows. 


Numbers  expressed  in  the         Numbers  expressed  in  the 
radix  of  10.  radix  of  12. 


9  9 

10  £ 

11  e 

12  i 

13  II 

18  16 

19  17 

20  18 

21  19 

22  i£ 

23  ie 

24  20 

25  21 

60  c0 


20  ELEMENTS   OF   SCIENCE 

Numbers  expressed  in  the         Numbers  expressed  in  the 

radix  of  10.  radix  of  12. 

TOO  84 

144  1 20  (i  2  times 

12) 

1728  1440 

Bui  instead  of  10  or  12,  we  might  make  use  of  a 
binary  system  of  notation,  that  is,  we  might  take  2  as 
the  radix.  Then  to  express  numbers  according  to  such 
a  system,  an  additional  figure  would  have  to  be  added  to 
the  right  for  every  increase  of  2,  as  follows  : 

Radix  of  10.  Hadix  of  2. 

0  o 

1  ;   I 

2  10 

3  ii 

4  100 

5  i°i 

6  no 

7  in 

8  1000 

9  1001 

10  1010 

11  ion 

Thus  according  to  this  system  every  time  the  symbol 
one  is  moved  one  space  to  the  left,  its  value  is  doubled — 
as  we  see  above  (in  the  radix  of  2),  where  10  is  twice  i  ; 
100  twice  the  value  of  10,  and  1000  twice  the  value  of 
100. 

If  we  square  (multiply  by  itself)  this   last  number 


MATHEMATICS  21 

n,   in   the   radix   of    two,   we   produce   the   following 
result : 

ion 

ion 

ion 
ion 

0000 
IOII 

IIIIOOI 

This  may  be  proved  to  be  right  by  analysing  the 
product  and  comparing  it  with  a  similar  analysis  of  1 1 
times  ii  in  the  system  of  the  radix  10. 

Radix  of  2.  Radix  of  10. 

1  =            1                              I 

I  GOO  2A              8 

10000  24             l6 

1 00000  2'5             32 

1000000  2°             64 


IIIIOOI  121 

Now  1111001  is  ii  multiplied  by  itself  according  to 
the  radix  of  2.  But  121  is  also  n  multiplied  by  itself 
according  to  the  radix  10  : 

ii 
ii 


ii 

ii 


121 


22  ELEMENTS   OF   SCIENCE 

Various  symbols  are  used  to  denote,  not  quantities, 
but  certain  relations  between  them.  Thus  the  symbol 
«=  shows  and  indicates  "  equal  to."  Other  symbols  are 
useful  as  follows : 

+  (plus,  or  added  to)  -  (minus,  or  taken  from) 

x   (multiplied  by)  4-  (divided  by) 

Thus  6  +  3  =  9.      9-4  =  5-      3x2  =  6.      10-4-5  =  2. 

These  signs  are  of  special  use  in  algebra,  as  we  shall 
shortly  see. 

This  explanation  of  the  fundamental  conceptions  and 
simplest  practices  of  the  arithmetical  part  of  mathe- 
matics will  suffice  for  our  purpose,  which  is  but  to  show 
(i)  what  are  the  truths  at  once  the  simplest  and  the 
most  universal,  because  applicable  to  all  objects  which 
can  be  enumerated,  and  (2)  to  make  if  clear  that  by 
working  with  such  symbols  we  can  arrive  at  definite 
results  which  correspond  (with  perfect  exactness  and 
certainty)  to  real  relations  existing  between  objects  of 
all  kinds. 

For  information  respecting  the  manifold,  complex,  and 
most  ingenious  processes  and  devices  whereby  the  labour 
of  counting  and  calculating  is  lightened,  the  reader  is 
referred  to  explicit  treatises  on  the  rules  and  practice 
of  arithmetic. 

Arithmetic  concerns  itself  with  definite  numbers, 
whole  or  fractional,  and  each  symbol  it  employs  denotes 
some  quantity  or  other.  But,  since  the  Middle  Ages,  a 
much  wider  and  more  searching  branch  of  mathematics 
has  been  widely  cultivated — namely,  Algebra. 

Each  arithmetical  operation  applies  only  to  certain 
numbers,  but  each  algebraic  operation  is,  at  one  and  the 
same  time,  good  for  all  numbers,  whole  or  fractional — 


MATHEMATICS  23 

i.e.,  for  indefinite  quantities  of  all  kinds,  known  and 
unknown. 

Algebra  is  a  further  extension  of  that  process  of 
abstraction  which  is  employed  in  arithmetic.  In  arith- 
metic we  use  symbols  to  denote  definite  quantities  of 
undefined  things.  Thus,  we  use  7,  9,  and  12  to  denote 
such  definite  quantities  of  any  kind  of  things  whatever. 
In  algebra  we  use  symbols  to  denote  undefined  quan- 
tities of  undefined  things.  An  algebraic  statement — 
e.g.,  a  +  a=2a — applies  to  any  possible  quantities  or  any 
possible  or  impossible  things.  That  economy  of  human 
effort  which  is  effected  by  arithmetic  is,  as  before  said, 
carried  to  enormously  greater  extent  by  algebra. 

Such  indefinite  quantities  as  are  treated  of  in  algebra 
are  represented  by  letters.  It  is  usual  in  elementary 
algebra  to  represent  definite  and  constant  quantities  by 
the  first  letters  of  the  alphabet,  a,  b,  c,  d,  &c.,  and  to 
represent  quantities  which  are  variable,  are  under  in- 
vestigation, and  have  to  be  determined,  by  the  last 
letters  of  the  alphabet,  z,  y,  x,  w,  &c. 

Capital  letters,  Greek  letters,  and  various  other 
symbols,  are  used  to  denote  quantities  according  to  cir- 
cumstances. As  to  symbols  denoting  relations  between 
quantities,  in  addition  to  those  lately  referred  to  as  of 
special  use  in  algebra,  the  following  may  be  added  out 
of  a  variety  of  other  ones  :  The  sign  >  between  two 
quantities  signifies  that  the  quantity  expressed  on  the 
left  hand  of  the  sign  is  greater  than  that  on  its  right,  as 
a  >  b  means  that  a  is  greater  than  b. 

Similarly,  a  <  b  means  that  the  right-hand  quantity 
(here  a)  is  less  than  that  on  the  left  hand. 

When  letters  representing  quantities  are  enclosed  in  a 
bracket,  or  have  a  line  drawn  over  them,  each  of  these 
symbols  signifies  that  such  quantities  are  to  be  taken 


24  ELEMENTS   OF   SCIENCE 

as  one  whole,  or  collectively.  Thus,  instead  of  writing 
axx  +  bxx*  +  cxx,  we  may  write  (a  +  b  +  c)x,  the  x  being 
placed  outside  the  bracket.  This  means  that  the  whole 
of  the  quantity  contained  within  the  bracket  is  to  be 
multiplied  by  x.  We  may  express  the  same  thing  thus  : 


cx  x. 

The  sign  .-.  means  therefore,  and  the  sign  v  means 
because. 

Numbers  as  well  as  letters  may  be  used  in  algebra. 
Thus,  2a  +  46  -  30  would  represent  18,  if  a  —  2,  b  =  8,  and 
c  =  6,  for  twice  2  are  4,  and  four  times  8  are  32,  and 
those  two  numbers  added  make  36,  while  if  three  times 
6,  which  is  18,  be  taken  away  (as  the  minus  sign 
indicates)  there  remains  18. 

Such  numbers  or  letters  prefixed  to  symbols  of  quan- 
tities, are  called  "  coefficients." 

Fractions    are   written   as   in    arithmetic  :    e.g.,   the 

number  a  of  any  denomination,  b  is  written  r- 

If  the  denominator  be  a  power  of  any  quantity — as 
~i>  or  -g>  or  ~v  then  such  a  quantity  may  be  expressed 

in  algebra  by  what  is  called  a  "  negative  power  "  of  such 
quantity,  that  is  by  a  corresponding  index*  with  the 
negative  sign  before  it. 

Thus,  -j  may  bet  written  a'1. 


~ 
"      a" 

(n,  of  course,  standing  for  any  number.) 


*  See  ante,  p.  15.  t  See  bottom  of  p.  25. 


MATHEMATICS  25 

Points  are  made  use  of  to  denote  proportion,  thus — 
A  :  b  :  :  c  :  d  signifies  that  a  bears  the  same  proportion  to 
b  as  c  does  to  d. 

There  are  certain  evident  truths  or  simple  axioms 
which  the  student  must  bear  in  mind,  thus : 

1.  If  equal  quantities  be  added  to  equal  quantities, 
the  sums  will  be  equal. 

2.  If  equal  quantities  be  taken  from  equal  quantities, 
the  remainders  will  be  equal. 

3.  If  equal  quantities  be  multiplied  by  the  same,  or 
equal  quantities,  the  products  will  be  equal. 

4.  If  equal  numbers  be  divided  by  the  same,  or  equal 
quantities,  the  quotients  will  be  equal. 

5.  If  the  same  quantity  be  added  to  and  subtracted 
from  another,  the  value  of  the  latter  will  not  be  altered. 

6.  If  the  same  quantity  be  used  both  to  multiply  and 
divide  any  quantity,  the  value  of  the  latter  will  not  be 
altered. 

It  may  be  useful  here  to  observe  that  the  signs  +  and 
-  ,  have  in  our  day  acquired  an  exceedingly  wide  significa- 
tion. They  are  now  used  to  denote  all  sorts  and  kinds  of 
opposition,  not  only  with  regard  to  quantity,  but  oppo- 
site relations  of  all  kinds — time,  space,  velocity,  or  any 
other  property.  So  if  +  be  applied  to  any  operation  t 
direction,  or  quality  then  -  will  denote  the  inverse 
operation,  the  opposite  direction  and  the  most  opposed 
quality.  Thus  if  +  refers  to  North,  to  increase,  to 
stability,  &c.,  -  will  denote  South,  decrease,  instability, 
&c. 

A  specially  algebraic  illustration  may  be  derived  from 
the  fact  that  since  a  means  a  times  any  unit,  a1  which  is 
a  taken  one  time,  signifies  i  multiplied  by  a,  and  since 
the  negative  sign  denotes  the  opposite  operation  a~l 
must  denote  i  divided  by  a. 


26  ELEMENTS   OF   SCIENCE 

Owing  to  the  extremely  wide  significance  these 
symbols  have  acquired,  it  is  now  also  very  common  to 
use  for  either  +  and  -  the  term  "  sense "  instead  of 
11  signs"  i.e.,  "  positive  sense  "  for  + ,  and  "  negative 
sense  "  for  -  . 

Algebraic  addition  is  partially  like,  yet  in  some 
respects  different  from,  arithmetical  addition. 

If  similar  quantities  have  different  signs,  then  their 
difference  must  be  taken  into  account  when  they  are 
added  together. 

Thus,  if  to     a  +  b 

a  —  b  be  added, 

the  result  is  2  a 

because  the  +  b  and  the  —  b  neutralise  each  other,  while 
each  a  remains. 

Similarly,  if  there  are  co-efficients,  their  differences 
must  be  taken  into  account.  Thus,  by  adding  together 

3«2  +  460  -  e2  +  10 
-  5«2  +  6bc  +  2e2  -  15 
—  &2  +  6bc  -  ioe2  +  21 


we  obtain         -  6a2  +   1 6bc  -    ge2  +  1 6      as  the  result. 

Though  convenient,  it  is  not  necessary,  to  write  the 
same  letters  over  each  other,  but  similar  quantities 
must  be  collected  together  in  stating  the  result, 
thus  : 

ax*  +  cz  +  by* 
2bx*  +  cyz  +  az 

-  z  +  xz  +  ?/2 


ax   +  2c   +  x    +          +  c      +        +  cz  +  az  -  z 


This  may  be  written  more  shortly  and  conveniently  by 


MATHEMATICS  27 

using  brackets,  since  y?  is  taken  a  times,  2  b  times  and 
once ;  and  if  is  taken  b  times,  and  c  times  and  once ;  and 
z  is  taken  c  times,  and  a  times  and  minus  once  ;  we  may 
evidently  write  it  with  the  result  as  follows : 

(a  +  2b  +  i)  y?  +  (b  +  c  +  i)  y2  +  (c  +  a  -  i)  z. 

Thus  the  addition  of  algebraical  quantities  is  per- 
formed by  connecting  those  that  are  unlike  with  their 
proper  signs,  and  collecting  those  that  are  similar  into 
one  sum. 

In  algebraical  subtraction,  on  the  other  hand,  we  have 
to  change  the  sign,  and  then  proceed  as  in  addition. 

The  reason  of  this  change  of  sign  is  best  seen  by  an 
example ;  and  the  reader  must  bear  in  mind  the  fifth 
axiom  before  given. 

Let  us  suppose  that  from  any  quantity  a,  there  has  to 
be  subtracted  the  quantity  b  —  c.  Now  if  we  subtract  b 
from  it  (which  would  be  expressed  thus,  a  -  b ),  we  shall 
have  subtracted  too  much,  because  the  quantity  to  be  sub- 
tracted was  not  b,  but  only  whatever  might  be  left  of  b 
after  c  had  been  taken  away  from  it,  It  was  not  the  whole 
sum  of  5,  but  only  b  diminished  by  c,  or  b  -  c,  which  had 
to  be  taken  from  a :  therefore  evidently  the  operation 
will  be  completed  by  adding  c  to  the  too  much  dimin- 
ished sum,  a  -  b. 

Thus  we  have  a  —  b  +  c,  and  so  we  have  come  to  change 
the  sign  before  c  from  —  into  + .  It  follows  that,  to 
subtract  b  -  c  from  a,  we  must  change  the  signs  and  add. 

Therefore  in  order  to  subtract  from 

+  a 
the  sum    +  b  -  c 

we  must  change  the  signs  of  the  quantities  to  be  sub- 
tracted ;  thus : 


28  ELEMENTS   OF   SCIENCE 

+  a 

-  b  +  c  and  then  add ; 
when  we  have  for  result    +  a  —  b  +  c,  which  is  correct. 

Any  quantity  preceded  by  the  sign  -  is  a  negative 
quantity. 

On  the  rational  principle  of  our  language,  that  "  two 
negatives  make  an  affirmative,"  to  take  away  a  negative 
quantity  from  any  other  quantity  is  really  to  add  to  that 
second  quantity.  Thus  if  5  has  been  taken  from  12, 
so  that  7  remains,  and  then  that  operation  be  negatived, 
that  amounts  to  adding  5  again  to  the  7  and  so  restor- 
ing the  original  number  12. 

Similarly,  if  both  2  and  3  have  to  be  taken  from  10, 
we  may  write  it  10  -  (2  +  3)  =  5.  But  if  no  bracket  be 
used,  we  must  of  course  change  the  sign  in  order  to  show 
that  both  2  and  3  are  taken  from  10,  and  write  it, 
10-2-3  =  5;  10-2  being  8,  and  8-3  being  5. 

Suppose  we  have  to  subtract  +  by  from  +  ^ax,  the 
difference  is  obviously  $ax-by\  and  thus  the  sign  before 
by  is  changed;  but  if  instead  of  the  positive  quantity 
+  by  we  have  to  take  the  negative  quantity  -  by  from 
+  sax,  the  result  then  must  be  ytx  +  by. 

This  may  seem  at  first  paradoxical  to  some  readers, 
but  to  take  away  a  negative  (i.e.,  to  subtract  a  dimi- 
nution) is  evidently,  in  fact,  to  make  an  addition.  To 
cause  a  man  to  cease  to  have  no  hat  is,  of  course,  to 
cause  him  to  have  one. 

The  above  statement  may  be  made  more  plain  by  the 
fifth  axiom,  for  if  we  both  add  and  subtract  the  same 
quantity  to  and  from  $ax,  then,  of  course,  $ax  will 
remain  unchanged  and  as  it  was.  Now  if  we  accord- 
ingly add  to  and  take  from  it  cy,  we  shall  have 
^ax  +  cy  —  cy,  which  is  simply  the  same  quantity  as  $ax. 
Let  us  then  take  -  cy  from'  both,  and  the  result  must 


MATHEMATICS  29 

(according  to  the  2nd  axiom)  be  the  same  in  each  case. 
But  if  we  take  -  cy  from  ^ax  +  cy  -  cy,  the  result,  of 
course,  is  $ax  +  cy.  Therefore,  if  we  take  -  cy  from 
$ax,  the  result  must  also  be  $ax  +  cy. 

From  ax3  -  bxz  +   x 
Take  px3  -  qx*  +  2x 

The  result  or  difference  =  (a  -  p)  xs  —  (b  -  q)xz  +  (i  -  2)  x. 

Here  we  have  the  quantity  XB  twice  repeated,  each 
time  with  a  different  coefficient,  and  the  coefficient  +j9, 
has  to  be  subtracted  from  +  a,  the  result  necessarily 
being  ax3  -px3,  which  may  be  written  (a  -p)  x3. 

Of  the  two  squares  of  x,  the  negative  coefficient  —  q, 
has  to  be  taken  from  -  b ;  we  must  then,  as  before,  change 
the  sign  of  q  for  subtraction,  and  so  we  have  -  bx*  +  qxz, 
and  this  may  be  expressed  in  a  bracket  —  (b  —  q  *)  x*. 
Finally  the  simple  quantity  x  and  the  coefficient  2  have 
to  be  subtracted  from  the  quantity  ix  (since  x  standing 
alone  is  one  x)  and  so  we  have  (i  -  2)  x. 

In  algebraic  multiplication  the  explicit  sign  of  that 
process  (  x  )  is  often  omitted,  and  any  two  letters  written 
with  only  a  point  between  them  (a. b),  or  merely  side  by 
side  (or  ab)  mean  (as  in  arithmetical  multiplication) 
that  a  has  to  be  taken  b  times,  or  that  b  has  to  be  taken 
a  times. 

If  the  quantity  which  is  to  be  multiplied  (or  the 
multiplicand),  and  the  quantity  by  which  it  has  to  be 
multiplied  (or  the  multiplier)  have  both  the  same  sign 
(both  +  or  both  - ),  then  the  result  must  have  the 

*  The  portion  b  remaining  after  q  has  been  subtracted  from 
it,  or  (b-q),  being  of  course  equal  to  that  produced  by  the 
subtraction  of  the  whole  of  b,  followed  by  the  addition  of 
q,  or  -  b  +  q. 


30  ELEMENTS   OF  SCIENCE 

positive  sign  (  +  )  prefixed  to  it.  If  they  are  unlike, 
then  the  result  must  have  the  negative  sign  (  — )  before 
it.  Thus  +  a  x  +  b  =  +  ab ;  -ax  +  b  =  -  ab; 
+  a  x  —  b  =  -  ab,  and  —  ax  -b  =  +ab. 

The  reason  of  this  is  very  simple,  +  a  x  +  b  =  +  ab, 
because   a   has  to   be    taken   positively   b   times;    and 

—  a  x  +  b=  —  ab,  because  the  sum  —  a  has  to  be 
taken  b  times,  as  is  expressed  by  the  result.  But 

+  a  x  —  b  also  =  —  ab,  because  multiplication  being,  as 
before  said,  essentially  the  same  as  addition,  multiplying 
a  by  b  is  the  same  thing  as  adding  a  to  itself  b  times. 
Now,  in  this  case,  a  has  to  be  added  to  itself  -  b  times, 
which  is  of  course  less  than  once,  or,  in  other  words  is 
really  subtraction.  Thus,  in  this  negative  case,  a  has 
to  be  subtracted  from  itself  b  times,  and  (as  we  have 
seen  in  subtraction)  the  sign  must  be  changed  and 
so  a  subtracted  from  itself  b  times  is,  and  must  be 

—  ab.     Lastly    —  a  x  -  b  =  +  ab,   because   here,   on 
the  same  principles  as  in  the  last  case,    -a  has  to  be 
subtracted  from  itself  b  times.     Therefore  it   is    -ab 
which  has  to  be  subtracted ;  but,  as  we  have  seen,  to 
subtract   a   negative   quantity   is   the    same    thing   as 
adding  a  positive  one,  and  therefore  subtracting  -ab 
is   the   same    thing    as    adding    +  ab,    and    therefore 

-ax  -  b  =  +  a  b. 

It  may  be  useful  to  note  the  three  following  examples 
of  multiplication : 

a  +  b 
multiplied  by  a  +  b 

a2  +    ab 
+    ab  +  bz 

a   +  2ab  +  62 


MATHEMATICS  31 

Therefore   here   we  see  what   is  the   square  of   the 
quantity  a  +  b  or  (a  +  b)2. 

Therefore  also,  the  square  root  of  the  product,  or, 


»J<&  +  2  a  b  +  6a  =  a  +  b. 

Again,  if  a   +  b 

be  multiplied  by  a   —  b 


a2  +  ab 

-  ab  -b* 

The  product  equals  a*  —  b* 

since  +  ab  and  -  ab  neutralise  each  other. 
If  we  multiply      i  -  x  +  cc2  -  x3 
by      i  +  x 

I    —  X  +  X2  —  XS 

+  x  -  x*  +  xs  -  x* 
The  result  is         i  -  x* 

The  other  quantities  neutralise  each  other. 

In  algebraical,  as  in  arithmetical,  division,  the  question 
is  to  determine  how  many  times  one  quantity,  "the 
divisor,"  may  be  contained  in  another,  "the  dividend," 
which  is  equivalent  to  finding  out  what  quantity  multi- 
plied by  the  divisor  will  produce  the  dividend. 

Thus  to  divide  ab  by  a,  is  to  determine  how  often  a 
must  be  taken  to  make  up  ab ;  that  is,  what  quantity 
multiplied  by  a  will  give  ab,  and  this  we  know  to  be  b. 

The  signs  change  as  they  do  in  multiplication,  and  for 
the  same  reason.  If  the  divisor  and  dividend  have  like 
signs  the  quotient  is  +  ;  but  - ,  if  they  have  unlike 
signs. 

Thus  -  ab  divided  by  -  a  =  b ;  because  -  a  (the 
divisor)  and  +  b  (the  quotient)  if  multiplied  together 
give  -  ab  (the  dividend). 


32  ELEMENTS   OF   SCIENCE 

If  we  divide  a?  +  2ab  +  b*  by  a  +  b  (its  square 
root  as  we  just  saw*)  the  quotient  must  equal  the 
divisor,  thus : 

a  +  b)  a?  +   2ab  +  I?  (a  +  b 
c?  +     ab 


ab  +  b* 
ab  +  b* 


Sometimes  quantities    may   be    continued  on  indefi- 
nitely, as  when  i  is  divided  by  i  —  x. 

i  -  x)  i          (i  +  x  +  x*  +  x9  &c.  &c. 


+  x 

+   X   - 


+   X* 

+  re2  -  x5 


+  x3  -  x* 

+  a?4,  &c.  &c. 


The  foregoing  observations  must  suffice  as  a  first 
introduction  to  the  principles  of  algebra,  as  a  branch 
of  science  replete  with  the  most  beautiful,  complex, 
ingenious,  and  far-reaching  processes,  whereby  alone 
many  calculations  are  made  possible,  or  the  labours  of 
investigation  lessened,  while  the  results  arrived  at  have 
extraordinary  accuracy.  Though  for  these  purposes  we 
may  employ  not  only  purely  imaginary,  but  even 

*  See  ante,  p.  31. 


MATHEMATICS  33 

impossible  quantities,  yet  the  results  of  the  facts  and 
laws  thereby  discovered  (like  those  of  arithmetic)  corre- 
spond with  the  facts  and  laws  of  real  or  possible 
existences.  They  express  abstract  truths  which  have 
real  applications  or  would  have  them  could  the  im- 
possible conditions  sometimes  supposed  really  exist.  Thus 
even  the  absurd  and  impossible  quantity  expressed  by  the 
symbol  J  —x  has  its  relation  with  reality.  It  is  really 
impossible  in  itself,  since  there  is  no  quantity  which, 
being  multiplied  by  itself,  gives  a  negative  product.  Yet 
it  has  its  relation  with  reality,  inasmuch  as  it  can  be  used 
as  if  it  were  a  real  quantity,  and  all  the  laws  and  relations 
relating  to  real  quantities  can  be  applied  to  it.  Thus  : 


Thus  we  may  investigate  laws  concerning  space, 
motion,  pressure,  &c.,  apart  from  certain  conditions 
which  in  fact  always  exist,  but  which  may  be  tem- 
porarily disregarded. 

The  results  so  arrived  at  will  be  absolutely  true, 
though  of  course  they  will  not  correspond  with  the 
phenomena  of  the  world  about  us,  till  we  take  into 
consideration  the  conditions  which  before  had  been 
purposely  left  out  of  the  calculation.  These  being 
correctly  restored  and  added,  the  results  will  correspond 
with  the  realities  of  experience. 

The  truths  and  processes  of  algebra  may  be  tested  by 
selecting  any  numbers  as  representatives  of  the  alge- 
braic symbols  (which  latter  are  valid  for  all  numbers) 
and  treating  them  similarly.  This  translates  the  results 
into  arithmetic,  and  arithmetical  results  may  then  be 
tested  by  experiments  with  corresponding  numbers  of 
material  bodies. 

Thus  as  an  example  of  the  correspondence  of  alge- 

C 


34.  ELEMENTS   OF  SCIENCE 

braic  truths  with  arithmetical  ones,  let  us,  for  example, 
represent  a  by  2  and  b  by  3. 

We  now  know  that  a  +  b  multiplied  by  a  +  b  equals 


-  Similarly  (2  +  3)  x  (2  +  3)  =  2*  +  2  (3x2)  +  32. 
j  For  2  +  3  =  5  and  5x5  =  25. 
Also  22  =  4,  while  2  (3  x  2)=  12  and  32  =  9. 
And  4+12  +  9  =  25. 

(  The  sciences  of  numbers  and  quantity  apply,  as  before 
said,  to  all  things  without  exception.  A  less  universal 
branch  of  mathematics  relates  to  all  things  with  length, 
breadth,  and  thickness.  This  is  geometry.  A  brief 
account  of  its  simplest  truths  will  serve  to  conclude 
our  introduction  to  the  elements  of  mathematical 
sciences. 

,  The  simplest  way  of  introducing  the  reader  to  the  ele- 
ments of  geometry  will  be  to  explain  a  proposition  of 
Euclid.  The  first  of  his  propositions  solves  the  problem 
how  to  draw  an  equilateral  triangle  (i.e.,  one  all  the 
three  sides  of  which  are  equal)  upon  a  given  straight 
line  of  a  certain  definite  length. 

To  do  this  we  must  take  the  following  premisses  for 
granted  : 

1.  That  a  straight  line  may  be  drawn  from  one  point 
to  another  ; 

2.  That  a  circle  may  be  drawn  from  any  given  centre 
at  any  practicable  distance  from  it  ; 

3.  That  a  circle  is  such  a  figure  that  all  straight  lines 
drawn  from  its  centre  to  its  circumference  (i.e.,  to  the 
single  line  which  bounds  it)  are  equal  to  one  another  ; 
and, 

4.  That  things  which  are  equal  to  the  same  thing  are 
equal  to  each  other. 

These  truths   (which  are  some  of  the  definitions  and 


MATHEMATICS 


35 


axioms  *  of  Euclid)  being  granted,  the  problem  is  solved 
as  follows,  and  the  reader  will  see  that  the  solution  is 
absolutely  certain  for  any  such  possible  triangle. 

Let  us  first  draw  a  line  (as  from  premiss  i  we  can) 
from  a  point  marked  A  to  a  point  marked  B,  and  let 
this  be  the  given  line  whereon  the  equilateral  triangle 
is  to  be  drawn. 

Now  taking  the  point  A  as  a  centre,  let  us  describe 
round  about  it  (as  from  premiss  2  we  can)  a  circle,  the 

FIG.  2. 


circumference  of  which  shall  pass  through  the  point  B 
forming  the  circle  BCDEF.  Next,  taking  the  point 
B  as  a  centre,  let  us  describe  round  about  it  a  circle, 
the  circumference  of  which  shall  pass  through  the  point 
A,  forming  the  circle  ACGHI.  From  the  point  C, 
where  these  two  circles  intersect,  let  us  draw  two  straight 
lines,  one  from  C  to  A  and  the  other  from  C  to  B,  as 
we  may  do  from  premiss  i. 


*  See  ante,  p.  25. 


36  ELEMENTS   OF   SCIENCE 

Then  the  triangle  ACB  will  be  the  triangle  required, 
i.e.,  it  will  be  an  equilateral  triangle  drawn  upon  a  given 
straight  line  of  a  certain  definite  length — namely,  from 
AtoB. 

This  is  and  must  be  so,  for  the  following  reasons : 

Since  A  is  the  centre  of  the  circle  BCDEF,  it  follows, 
from  premiss  3,  that  the  two  lines  AB  and  AC  must 
be  equal,  since  they  are  both  lines  which  pass  from  the 
centre  to  the  circumference  of  the  same  circle,  i.e.,  the 
circle  BCDEF. 

Similarly,  because  B  is  the  centre  of  the  circle  ACGHI, 
the  lines  AB  and  BC  must  be  equal,  because  they  both 
pass  from  the  centre  to  the  circumference  of  a  circle, 
i.e.,  of  the  circle  ACGHI. 

But  we  have  already  seen  that  the  line  AC  is  equal 
to  the  line  AB,  therefore  (by  the  4th  premiss)  the  line 
A  C  must  be  equal  to  the  line  BC — since  both  AC  and 
BC  are*  each  equal  to  AB.  It  follows  then  that  the  three 
lines  AB,  AC,  BC,  are  equal  to  one  another.  Therefore 
the  triangle  they  form  is  an  equilateral  one  described 
upon  a  given  straight  line  of  a  definite  length — namely, 
upon  the  line  AB. 

Proofs  analogous  to  the  above,  support  all  the  proposi- 
tions of  Euclid,  and  the  results  are  absolutely  certain  and 
true.  In  nature,  the  properties  of  bodies  as  regards 
their  occupation  of  space — or,  as  it  is  called,  their  "ex- 
tension"— correspond  as  accurately  with  the  laws  of 
geometry  as  their  material  conditions  render  possible. 
Obviously  the  lines  and  surfaces  which  can  be  made  in 
some  substances  are  less  definite  and  exact  than  those 
which  can  be  formed  in  others,  and  in  no  substance  can 
lines  and  surfaces  of  ideally  perfect  straightness,  &c.,  be 
produced. 

But  such  deviations  from  ideal  perfection,  in  no  way 


MATHEMATICS  37 

invalidate  the  absolute  truth  of  the  determinations  of 
geometry  themselves,  which  are  more  accurately  con- 
formed to,  the  more  the  nature  of  any  material  ren- 
ders it  able  to  approach  more  nearly  to  the  perfection 
desired. 

Geometry  arose  through  desires  and  efforts  to  measure 
land  accurately,  and  the  properties  of  angles  and  triangles 
actually  serve  this  process  now.  One  of  the  most  useful  pro- 
perties of  triangles  consists  in  the  fact  that  two  of  them, 
however  different  in  size,  are  in  other  respects  exactly 
similar  to  each  other  if  the  angles  of  one  are  severally 
equal  to  the  angles  of  the  other.  It  is  by  the  aid  of 
such  considerations  that  many  of  the  most  important  and 
prodigious  scientific  measurements  have  been  effected.* 

Euclid's  work  treats  not  only  of  lines,  angles,  triangles, 
circles,  &c.,  but  of  the  geometrical  properties  of  solid 
figures  of  several  different  shapes. 

Greek  geometers  occupied  themselves,  in  a  purely 
speculative  manner,  with  the  different  methods  in  which 
a  circular  cone  may  be  cut.  The  investigation  of  the 
various  kinds  of  curves  which  may  be  produced  at  the 
edge  of  such  a  cone  by  cutting  across  t  it  in  different 
directions,  constituted  the  study  known  as  "  Conic 
Sections."  The  importance  of  these  investigations  will 
become  clear  when  we  have  to  consider  falling  and  other 
movements  of  various  bodies. 

Very  many  geometrical  propositions  which  were  long 
thought  incapable  of  investigation  and  solution  save  by 
the  method  proper  to  geometry,  were  subsequently 
found  capable  of  more  convenient  treatment  by  the  aid 
of  algebra,  a  change  which  has  produced  most  impor- 
tant results  in  the  study  of  astronomy. 

*  See  post,  p.  177.  f  See  post,  p.  65. 


3&  ELEMENTS   OF  SCIENCE 

Even  the  beginner  may  see  how,  in  some  instances,  a 
geometrical  proposition  may  be  more  conveniently  treated 
algebraically.  Thus,  e.g.,  there  is  one  *  which  declares 
that  if  a  right  line  be  divided  into  any  two  parts,  the 
square  of  the  whole  line  is  equal  to  the  square  of  the  two 
parts  together  with  twice  the  product  of  those  parts. 

Now  evidently  this  is  equivalent  to  saying  that  if  we 
take  a  to  represent  one  of  the  two  parts  into  which  the 
right  line  is  divided  and  b  to  represent  its  other  part, 
then  the  square  of  the  whole  line  is  equal  to  the  squares 
of  a  and  b  together  with  twice  the  product  of  a  and  b, 
and  this  must  be  «2  +  2ab  +  fr2,  which,  as  we  saw  before,! 
is  the  result  of  multiplying  a  +  b  by  itself,  or  in  other 
words  is  equivalent  to  (a  +  6)2. 

Of  late  years  a  converse  process  has  taken  place,  and 
various  algebraic  processes  have  been  converted  into  geo- 
metrical demonstrations,  which,  as  less  highly  abstract, 
are  more  readily  apprehensible. 

By  a  number  of  elaborate  processes  (which,  however 
elaborate,  are  essentially  similar  to  and  wholly  based  upon 
the  elementary  matters  herein  pointed  out)  the  most 
varied  properties  of  objects  may  be  investigated,  includ- 
ing complex  reciprocal  relations  of  increase,  decrease,  and 
variation.  When  two  quantities  vary,  they  may  do  so 
equally  or  in  different  proportions  or  ratios.  When  one 
quantity  varies  with  another,  it  is  said  to  be  a.  function  of 
the  latter.  There  are  many  other  divisions  of  the  science, 
whereof  one  is  known  as  the  Differential  Calculus  ar.d 
deals  with  computations  concerning  the  rates  of  change 
between  quantities,  while  another,  called  the  Integral 
Calculus,  passes  from  the  relation  between  such  rates 
back  to  the  relations  existing  between  the  changing 

*  Euclid,  Book  II.,  Proposition  IV.  t  See  ante,  p.  30. 


MATHEMATICS  39 

quantities  themselves.  With  such  matters  the  highest 
branches  of  mathematics  are  concerned,  but  they  are,  of 
course,  quite  beyond  the  range  of  an  introduction  to  the 
elements  of  science. 

For  information  concerning  all  but  the  rudiments  of 
mathematics,  the  reader  is  referred  to  the  various  works 
specially  devoted  to  the  teaching  of  that  science. 

But  before  concluding  this  chapter  we  desire  again  to 
insist  on  the  correspondence  which  exists  between  the 
truths  of  mathematics,  of  whatever  order,  and  the  proper- 
ties of  real  substantial  things.  The  truths  of  geometry  are 
made  evident  to  the  eye  by  diagrams  and  to  the  mind  by 
reasoning.  The  truths  of  algebra  may,  as  before  said,* 
be  tested  by  taking  certain  numbers  as  exponents  of  the 
algebraic  signs,  and  so  reducing  algebra  to  arithmetic, 
while  the  truths  of  arithmetic  may  be  demonstrated  by 
the  seeing  and  handling  of  corresponding  numbers  of 
real  material  bodies.  We  may  now  pass  on  to  the  study 
of  elementary  truths,  second  only  to  mathematics  in  the 
universality  of  their  application. 

*  See  ante,  p.  33. 


CHAPTER    III 
MECHANICS 

HAVING,  in  the  preceding  chapter,  considered  the  first 
elements  of  that  branch  of  science  which  is  the  most 
universal  of  all  (since  it  relates  to  all  things  which  can 
be  counted),  we  may  now  proceed  to  make  some  acquaint- 
ance with  the  science  which  treats  of  the  next  most 
general  and  obvious  properties  and  powers  of  the  sub- 
stances and  bodies  which  make  up  the  world  about  us, 
namely,  with  the  science  of  Mechanics. 

We  have  hitherto  only  been  concerned  with  ideas 
of  number,  space,  and  direction,  but  in  mechanics  we 
shall  be  compelled  to  deal  with  time,  motion,  and 
force. 

All  bodies  known  to  us  may  be  roughly  arranged 
in  three  groups:  (i)  a  group  of  solids,  such  as  pieces 
of  stone,  metal,  wood,  &c. ;  (2)  a  group  of  liquids',  and 
(3)  a  group  of  substances  more  or  less  like  the  air  we 
breathe,  or  like  gas,  and  which  are  thence  termed 
aeriform  or  gaseous.  Liquids  and  gases  are  also  classed 
together  as  fluids,  on  account  of  the  ready  mobility  of 
both. 

Any  of  these  three  kinds  of  bodies  may  be  apparently 
in  a  state  of  rest,  or  obviously  in  motion,  and  the  study 
of  the  various  circumstances  which  attend  these  two 
conditions  of  such  bodies,  constitutes  the  "  Science  of 
Mechanics." 


MECHANICS  41 

As  every  one  knows,  solid  bodies  and  liquid  substances, 
when  unsupported,  fall  to  the  ground,  such  apparent 
exceptions  as  balloons,  <fcc.,  not  being  really  exceptions — 
as  will  be  seen  later  on.  We  say  that  bodies  are  "  heavy," 
and  that  it  is  their  weight  which  makes  them  fall.  But 
this  "  weight "  of  theirs  also  causes  them  to  press  with 
greater  or  less  force,  so  to  speak,*  on  whatever  supports 
them.  Many  things  (intentionally  or  unintentionally) 
are  thus  so  pressed  and  squeezed  that  they  become 
flattened  out — thus  making  such  pressure  evident  to 
our  senses. 

In  this  way  it  becomes  plain  that  most  (if  not  all) 
things  tend  to  fall,  not  only  to  the  general  surface  of  the 
ground  but  as  much  deeper  as  circumstances  may  render 
possible — as  water,  stones,  &c.,  will  be  sure  to  fall  to 
the  bottom  of  the  deepest  excavation,  unless  arrested  by 
something  which  checks  such  fall  and  sustains  the  falling 
bodies.  We  may  then  fairly  assume  that  whatever  tends 
to  fall,  tends  to  fall  towards  the  centre  of  the  earth. 

Therefore  everything  on  its  surface  which  appears  to 
be  (and  for  us  practically  is)  in  a  state  of  rest,  is  really 
tending  to  move  and  is  only  prevented  from  actually 
moving  by  some  other  object  which  checks  its  progress. 

But  we  know  that  some  things  topple  over  very  easily, 
while  others  remain  securely  at  rest.  A  die  will  lie 
steadily  on  whichever  side  it  falls,  but  if  we  heap  a 
number  of  dice  upon  each  other,  we  shall  soon  erect  such 

*  The  word  "force"  is  now,  in  strictness,  used  to  denote 
the  cause  of  motion,  and  "energy"  to  indicate  the  amount 
of  work  a  force  can  do.  To  enter  here,  however,  into  any 
controversy  as  to  the  uses  of  such  terms,  would  be  foreign 
to  the  purpose  of  a  work  which  proposes  only  to  introduce 
students  to  the  elements  of  science.  We  therefore  do  not 
hesitate  to  employ  a  popular  phraseology  when  it  seems  likely 
to  help  on  the  purpose  we  have  in  view. 


42 


ELEMENTS   OF   SCIENCE 


FIG.  3. 


a  pile  of  them  as  a  very  slight  disturbance  will  cause  to 
fall. 

In  very  stable  structures,  like  the  ancient  Egyptian 
buildings,  such  pressure  was  most  amply  provided  for, 
and  an  equilibrium  of  the  most  stable  kind  produced. 

This  was  the  case  above  all  with  the  Pyramids,  and  to 
a  less  degree  in  such  temples  as  those  of  Philse  and  Karnac 
— so  impressive  from  the  superfluous  strength  of  their 
many  rows  of  close-set,  massive  columns.  In  Grecian 

buildings  we  meet  with  the 
same  secure  repose,  but  in 
greater  delicacy  of  build.  In 
the  arch  and  the  dome,  how- 
ever, and  still  more  in  pointed 
architecture,  the  conflict  of 
stones  which  tend  to  fall  in 
different  directions,  produces 
(by  the  neutralising  of  each 
other's  thrusts)  a  different 
kind  of  equilibrium  and  one 
of  a  less  stable  character. 

As  every  one  knows,  sub- 
stances of  the  same  size  of 
various  kinds  may  be  very 
different  in  weight ;  as  we  see 

in  a  cube  made  of  cork  and  another  of  precisely  the 
same  size  made  of  lead,  or  two  glass  vessels  of  the  same 
size,  one  filled  with  water  and  the  other  with  quicksilver 


or  "  mercury." 


Heavier  bodies  are  said  to  be  more  dense  than  lighter 
bodies  of  the  same  size.  Thus  experiment  shows  us  that 
the  density  of  Mercury  is  13.6  times  that  of  water. 
Similarly  the  density  of  lead  is  much  greater  than  that 
of  wood.  Substances  also  differ  in  the  extent  to  which 


MECHANICS  43 

they  can  be  compressed  or  stretched  or  bent  or  twisted  ; 
as  to  the  degree  of  elasticity  they  possess,  or  as  to  the 
ease  with  which  they  can  be  broken.  They  differ,  besides, 
as  to  the  amount  of  resistance  (or  friction)  caused  by  the 
movement  of  one  upon  another. 

In  the  elementary  theoretical,  as  distinguished  from 
practical,  science  of  mechanics,  however,  the  consideration 
of  such  differences  is  omitted  in  order  to  reduce  problems 
to  their  simplest  form.  Solid  bodies  are  supposed  to  be 
incapable  of  any  change  of  form  and  perfectly  in- 
flexible, while  cords  are  treated  as  perfectly  supple  and 
entirely  devoid  of  any  rigidity.  Therefore  the  solids, 
fluids,  and  aeriform  bodies  of  mechanics,  are  imaginary 
substances,  and  not  such  as  we  actually  find  in  nature. 
But  the  consideration  of  these  qualities  and  properties 
(of  which  abstraction  is  thus,  for  convenience,  made)  can 
always  be  added,  and  so  the  results  of  the  science  (as 
we  saw  *  was  the  case  with  mathematics)  correspond, 
with  practical  exactness,  to  the  characters  and  properties 
of  real  material  things. 

Now  every  such  thing  may,  for  convenience,  be 
supposed  to  be  made  up  of  an  immense  number  of  most 
minute  and  uniformly  distributed  particles;  and  the 
influence  that  makes  it  fall — which  is  known  as  the/brce 
of  gravity,  or  gravitation — might  be  represented  by  lines 
drawn  from  every  such  particle  towards  the  centre  of  the 
earth.  But  as  such  lines  would  thus  converge  towards  a 
point  enormously  distant,  they  may  be  treated  as  if  they 
were  all  parallel  to  one  another. 

But  all  such  parallel  forces  (so  represented  by  lines) 
may  be  replaced  by  a  single  force — also  represented  by  a 
line — applied  to  a  certain  point,  and  such  point  is  called 

*  See  ante,  p.  33. 


44 


ELEMENTS    OF   SCIENCE 


"  the  centre  of  gravity  "  of  the  body — as  being  the  centre 
of  such  parallel  and  equal  forces — and  is  a  fixed  point 
which  does  not  change,  whatever  be  the  position  which 
the  solid  body  may  assume. 

In  order  that  a  body  should  be  in  equilibrium,  it  is 
necessary  for  it  to  be  supported  by  a  force  equal  to  the 
body's  weight  and  acting  through  its  centre  of  gravity  in 
a  direction  opposite  to  its  weight — as  in  the  architectural 
illustrations  just  given. 

In  a  cylindrical  body,  this  centre  is  in  the  middle  of  its 

FIG.  4. 


axis,  and  if  such  cylinder  be  obliquely  placed  (as  in  the 
Leaning  Tower  of  Pisa)  it  will  not  fall,  provided  the  weight 
at  the  centre  of  gravity  be  sustained — i.e.,  if  the  vertical 
line  from  it  to  the  ground  comes  within  its  basis  of  sup- 
port. If  it  passes  outside  this,  then  such  a  cylinder,  or 
building,  must  fall,  and  this  is  the  reason  why  a  very  high 
pile  of  dice  may  so  easily  be  made  to  topple  over;  because 
a  very  slight  inclination  will  carry  the  centre  of  gravity 
of  such  a  body  beyond  its  base.  Bodies,  of  course,  may 


MECHANICS  45 

remain  in  equilibrium  by  being  suspended — i.e.,  by  having 
the  weight  at  their  centres  of  gravity  supported  from 
above  instead  of  from  below. 

If  a  body  be  supported  in  such  a  manner  that  on 
its  equilibrium  being  disturbed,  it  tends  to  regain  it 
(as  in  an  oscillating  pendulum  or  a  detached  wooden 
ball  loaded  with  lead  at  one  place)  it  is  said  to  be  in 
stable  equilibrium.  In  the  opposite  case  (as  when  a  pole 
is  balanced  at  one  end),  the  equilibrium  is  unstable, 
because  when  disturbed,  it  tends  to  fall  further  away 
from,  instead  of  regaining,  the  position  in  which  the  ver- 
tical line  from  its  centre  of  gravity  falls  within  its  base. 

The  centre  of  gravity  is  not  necessarily  within  the 
solid  body  itself  which  has  to  be  supported,  but  may  be 
in  its  vicinity,  as  in  the  case  of  a  ring,  or  any  hollow 
vessel.  Thus  it  is  that  a  variety  of  posturing  tricks  can 
be  performed  in  tight-rope  dancing.  The  dancer  carries 
a  long  pole,  the  weight  of  which  transfers  the  centre  of 
gravity  to  the  middle  of  the  pole  within  the  grasp  of 
his  hands  so  that  he  has  it  under  his  control.  Similarly,  in 
balancing  rods  on  head  or  hand,  the  performer's  art 
consists  in  keeping,  by  means  of  constant  movement, 
the  base  of  the  rod  under  the  centre  of  gravity.  A 
number  of  ingenious  toys  are  also  constructed  on  the 
principle  of  an  external  position  for  the  centre  of 
gravity.  Thus  the  figure  of  a  prancing  horse  may 
be  made  to  rock  backwards  and  forwards,  resting, 
near  the  edge  of  a  table,  on  its  hind  feet  only,  in  an 
apparently  impossible  position,  by  means  of  a  leaden 
weight  at  the  end  of  a  curved  wire,  the  other  end  of 
such  wire  being  fixed  to  the  belly  of  the  horse,  so  that 
the  centre  of  gravity  of  the  whole  structure  is  thrown 
behind  and  below  the  prancing  figure.  Thus,  although 
its  position  looks  most  insecure,  its  equilibrium  is  really 


46  ELEMENTS   OF   SCIENCE 

quite  stable — namely,  that  of  an  ingeniously  contrived 
oscillating  pendulum. 

A  body  is  in  equilibrium,  or  a  state  of  rest,  when  the 
forces  which  act  upon  it  counterbalance  one  another. 
One  such  force  may  be  the  force  of  resistance  which  a 
supporting  body  offers  to  the  weight  of  the  body  which 
it  supports  and  so  keeps  in  equilibrium. 

As  numbers  and  quantities  may  be  represented  by 
arithmetical  or  algebraic  symbols,  so  forces  may  be 
represented  by  lines  of  definite  lengths.  These  will  be  the 
longer  the  greater  the  force  they  represent,  and  they  will 
also  serve  to  indicate  the  direction  of  the  forces. 

If  two  forces  be  in  equilibrium,  they  must  be  equal  in 
magnitude  and  opposite  in  direction.  It  is  plain  that 
if  such  were  not  the  case,  the  greater  of  the  forces  would 
overcome  the  other,  therefore  the  two  would  not  neutralise 
each  other,  and  so  we  should  have  motion,  and  not 
equilibrium. 

But  whatever  the  number  and  direction  of  the  forces 
which  may  act  upon  any  point,  they  can  only  produce 
motion  in  one  direction.  This  is  called  the  resultant  of 
such  forces,  which  are  the  several  components  of  this 
resultant. 

When  two  or  more  forces  act  on  a  point  in  the  same 
direction,  the  resultant  must  be  equal  to  their  sum,  and 
if  in  opposite  directions,  then  to  the  difference  between 
their  sums. 

Thus  if  any  point  be  pressed  upwards  by  a  force  of 
ten  pounds  and  downwards  by  a  force  of  five  pounds,  the 
resultant  must  be  a  pressure  upwards  of  five  pounds.  If 
the  pressure  towards  the  west  be  3  +  5  +  9,  while  that 
to  the  east  be  7  +  6  +  4  the  resultant  =17-17  or  o, 
which  is  equilibrium. 

As   to  direction,  let  the  equal  forces   A   and  B  act 


MECHANICS  47 

simultaneously  on  the  point  P,  the  force  PC  tending  to 
draw  the  point  P  towards  C,  and  the  force  PE  tending 
to  draw  the  point  P  towards  E,  then  if  from  the  two 
points  C  and  E,  equidistant  from  P,  we  draw  two  lines, 
CD  parallel  to  PE  and  ED  parallel  to  PC,  meeting 
at  D,  the  line  PD  will  be  the  diagonal  of  the  figure 
PCDE,  and  will  represent  the  resultant  of  the  two 
forces  A  and  B. 

The  points  C  and  E  have  been  here  made  equidistant 
from  P,  because  the   two   forces   are   supposed   equal. 
Were   they,  however,  unequal,  then   the   distance  PC 
FIG.  5. 

A  ~ 


B 


would  have  to  be  made  to  bear  the  same  proportion  to 
EP  as  the  force  A  has  to  the  force  B — a  unit  of  length 
representing  a  unit  of  force.  In  that  case,  instead  of 
forming  a  parallelogram  (i.e.,  a  straight-lined  quadri- 
lateral figure  whose  opposite  sides  are  equal  and  parallel) 
with  adjacent  sides  equal,  such  sides  would  be  unequal. 
Now,  it  is  a  rule  in  mechanics,  that  if  two  forces  acting 
at  a  point  be  represented  in  magnitude  and  direction  by 
the  sides  of  a  parallelogram,  the  resultant  force  will  be 
represented  in  magnitude  and  direction  by  the  diagonal 
of  the  parallelogram  passing  through  that  point. 

Any  number  of  forces  acting  on  a  single  point  can  be 


48  ELEMENTS   OF   SCIENCE 

computed  by  this  rule,  and,  inversely,  any  single  force 
may  be  considered  as  resolved  into  any  number  of  forces 
of  which  such  single  force  would  be  the  resultant.  The 
former  process  is  called  the  composition  and  the  latter 
the  resolution  of  forces,  and  both  processes  are  most 
frequently  employed  in  the  science  of  mechanics. 

In  a  system  of  balanced  or  statical  forces,  each  is  exactly 
equal  and  opposite  to  the  resultant  of  all  the  rest,  as  is 
shown  in  a  proposition  known  as  the  Polygon  of  Forces. 

Let  us  suppose  that  five  forces  are  all  acting  at  (from) 

FIG.  6. 


the  point  P,  while  their  respective  directions  and  in- 
tensities, are  represented  by  the  five  lines  PF1,  PF2,  PF3, 
PF4,  and  PF5,  passing  from  those  letters  to  P.  Construct- 
ing a  parallelogram  whereof  PF1  and  PF'2  are  two  sides, 
the  line  PC  will  be  their  diagonal  and  resultant.  Next 
taking  this  resultant  and  the  next  force  PF3  as  two  sides 
of  another  parallelogram,  we  find  that  PD  will  be  their  re- 
sultant, and  therefore  the  resultant  of  all  the  three  forces. 
Finally  taking  this  latter  resultant  and  constructing  a 
parallelogram  from  it  and  the  fourth  force,  we  find 


MECHANICS  49 

that  PE  is  the  resultant,  which  we  see  exactly  balances 
the  remaining  force  PF3.  Thus  is  formed  a  many-sided 
figure  or  polygon,  consisting  of  the  lines  PF1,  F1^  CD, 
DE,  and  EP,  the  five  sides  of  which  represent  the  five 
forces,  because  a  parallelogram  must  have  its  opposite 
sides  equal. 

PF1  expresses  the  intensity  of  the  force  acting 
along  PF1. 

FXC  expresses  the  intensity  of  F2,  because  FJC  is  the 
side  of  a  parallelogram  whereof  PF2  (expressing  the 
intensity  of  F2)  is  the  opposite  side. 

Similarly  CD  must  equal  PF3  and  DE  must  equal  PF4, 
while  PE  -  F5. 

There  may  be  two  forces  acting  side  by  side,  as  in 
a  two-horsed  carriage.  Two  such  powers  are  called 
parallel  forces.  The  resultant  of  two  parallel  forces 
acting  in  the  same  direction  is  equal  to  their  sum,  and, 
when  such  forces  are  equal,  the  resultant  of  their  com- 
bined force  acts  midway  between  the  points  of  application 
of  each;  when  unequal,  it  is  in  a  definite  degree  (as  we  shall 
shortly  see)  nearer  to  the  stronger  force. 

When  the  parallel  forces  are  equal  but  act  in 
opposite  directions,  their  result  is  to  produce  rotation, 
and  this  tendency  cannot  be  counterbalanced  by  any 
single  force. 

A  practical  knowledge  of  rudimentary  mechanics  was 
no  doubt  early  obtained,  since  human  ingenuity  would 
readily  suggest  the  application  of  a  strong  stick,  as  a  lever, 
to  raise  a  heavy  body  from  the  ground,  and  would  lead 
to  the  perception  that  it  is  easier  to  push  such  a  body 
up  a  sloping  surface,  than  to  raise  it  in  men's  arms  and 
carry  it.  Though  we^aiiitrteaduce  the  reader  but  to  the 
first  elements  of  mechanics,  we  must  nevertheless  offer 
some  explanation  with  respect  to  the  principle  of  the 


50  ELEMENTS   OF  SCIENCE 

lever,  the  inclined  plane,  and  the  pulley,  referring  him 
for  further  explanation  about  them  to  professed  treatises 
on  mechanics. 

To  return,  for  a  little  to  the  consideration  of  the 
action  of  two  parallel  and  unequal  forces : 

Let  us  suppose  that  a  heavy  rigid  bar  is  balanced  on  a 
point  at  its  centre,  which  must,  of  course,  be  its  centre 
of  gravity. 

Now  if  we  suppose  the  bar  to  be  made  up  of  two 
bars,  a  larger  one,  AD,  and  a  shorter  one,  DB,  then 
they  also  can  be  supported  at  their  respective  centres — 
namely,  at  D'  for  AD,  and  at  D"  for  DB.  But  the 
two  bars  thus  respectively  supported  at  D'  and  D",  act 
as  two  parallel  and  unequal  forces  (namely,  the  weight 
of  each),  and  their  resultant  must  pass  through  the  point 

FIG.  7. 

A  D1        C     D        D"       B 


A 


Y 


C,  because  it  is  at  that  point  that  their  two  pressures 
are  neutralised  by  the  support  which  balances  the 
whole.  Hence  we  see  that  the  resultant  of  the  two 
unequal  forces  does  not  pass  through  a  point  midway 
between  them  (i.e.,  mid-way  between  D'  and  D"),  but 
through  the  point  C,  which  is  much  nearer  to  D'  than 
to  D".  It  is  just  so  much  nearer  as  the  weight  of  AD 
is  greater  than  the  weight  of  BD.  That  is  to  say,  as 
D'C  :  D"C  : :  the  weight  of  BD  :  the  weight  of  AD. 
In  other  words,  the  resultant  of  the  two  unequal 
parallel  forces  is  so  situated  that  its  distance  from 
either,  shall  be  inversely  as  their  intensities.  To  prove 
the  truth  in  the  example  chosen,  we  may  suspend  from 


MECHANICS 


the  points  D'  and  D"  two  additional  weights  X  and  Y, 
bearing  the  same  ratio  to  each  other  as  the  weights 
of  AD  and  DB  had  previously  borne.  Then  the  balance 
will  still  remain  undisturbed  in  spite  of  the  greater 
weight  suspended  on  one  side  of  C  compared  to  that 
on  the  other  side  of  it. 

A  lever  is  a  rod  we  will  suppose  to  be  perfectly  rigid 


FIG.  8. 


W 


A 


W 


u 


fi 


F 


W 


HI 


(and  we  will  here  assume  it  to  be  also  straight), 
which  turns  on  a  fixed  point  called  the  fulcrum.  A 
force  is  applied  at  some  point  in  the  lever,  while  at  some 
other  point  there  is  a  resistance  acting,  which  resistance 
the  force  has  to  overcome.  The  portions  of  the  lever 
which  may  be  on  either  side  of  the  fulcrum  are  called 
the  arms  of  the  lever. 

Levers  may  be  of  three  orders:  a  lever  of  the  first 


52  ELEMENTS   OF   SCIENCE 

order  (I.  Fig.  8)  is  one  where  the  force  or  effort  acts  on 
one  side  of  the  fulcrum,  while  the  resistance  is  on  the 
other. 

A  lever  of  the  second  order  is  one  where  both  forces 
are  on  the  same  side  of  the  fulcrum,  while  the  point 
of  resistance  is  placed  between  the  fulcrum  and  the 
effort.  (II.  Fig.  8). 

A  lever  of  the  third  order  (III.  Fig.  8)  is  one  where 
the  two  forces  are  also  both  on  one  and  the  same  side 
of  the  fulcrum,  but  the  effort  acts  between  the  fulcrum 
and  the  point  of  resistance. 

FIG.  9.  One  of   the   most   useful 

applications  of  the  principle 
of  the  lever  is  that  employed 
in  thebalance,  which  is  a  lever 
of  the  first  order,  called  the 
beam,  suspended  at  its  centre 
and  with  its  two  arms  conse- 
quently equal. 

In  the  pulley,  we  have  an 
example  of  the  transmission 
of  force  through  a  cord  con- 
sidered as  perfectly  flexible 
— free  from  all  friction,  and 
inextensible. 

Thus  the  resistance  of  a  weight  suspended  at  one  end 
of  a  cord,  may  be  perfectly  balanced  by  a  force  (such  as  a 
sufficient  grasp  of  a  hand)  applied  at  the  other  end  of  a 
cord  which  has  been  passed  over  a  hook  and  through  a 
ring  (A,  Fig.  9). 

Such  forces  must  always  be  what  is  called  divergent, 
or  opposed  to  each  other,  and  by  such  an  arrangement 
the  direction  in  which  a  force  acts  may  be  changed 
without  modifying  its  intensity,  the  cord  being  supposed 


MECHANICS 


53 


always  to  undergo  the  same  tension  at  every  part  of  its 
length.  It  is  practically  convenient  to  use  a  pulley 
instead  of  a  hook  or  ring;  the  pulley  being  a  wheel  which 
turns  freely  on  an  axle  passing  through  its  centre,  with 
a  groove  at  its  circumference  for  the  reception  of  the 
cord.  Nevertheless  it  is  the  cord  and  not  the  pulley 
which  is  the  efficient  agent  in  this  mechanical  con- 
trivance. By  various  ingenious  arrangements  of  pulleys, 
a  very  small  force  may  be  made  to  overcome  a  great 
resistance,  as  for  instance  in  lifting  a  heavy  weight.  But 
for  a  description  of  these  the  reader  is  referred  to  pro- 
fessed treatises  on  mechanics. 

FIG.  10. 


The  inclined  plane  is  another  contrivance,  by  means 
of  which  a  weight  may  be  lifted  to  a  certain  height  by 
the  application  of  a  force  less  than  itself.  The  extent 
of  the  inclined  surface,  AB  (Fig.  10),  is  termed  the 
length  of  the  inclined  plane.  Its  height  is  repre- 
sented by  AC,  and  its  base  by  BC. 

Suppose  a  heavy  weight  W  to  be  supported  on  a 
smooth  inclined  plane  ABC  by  a  force  (weight)  P,  as 
in  the  figure — i.e.,  by  a  cord  passing  over  a  pulley  at  A. 
Then  it  will  be  seen  that  if  P  exactly  balances  W,  and 


54  ELEMENTS   OF   SCIENCE 

there  is  no  friction,  and  if  the  body  W  ascends  from 
B  to  A — i.e.,  if  it  rises  through  the  distance  CA — the 
weight  P  descends  through  a  distance  equal  to  BA ;  and 
by  comparing  P  with  W  it  will  be  found  that 

As  P  :  W  :  :  AC  :  AB. 

Consequently,  by  diminishing  the  height  of  the  plane, 
as  compared  with  the  length,  the  force  P  may  be  made 
as  small  as  we  please,  compared  with  W,  the  resistance 
to  be  overcome. 

We  have  hitherto  considered  force  with  respect  rather 
to  its  statical  effects  as  equilibrating  other  forces  ;  but 
force  is  manifested  in  its  most  interesting  aspect  in 
producing  motion — in  imparting  motion  to  what  we  call 
matter — the  study  of  which  is  dynamics. 

We  must  now  consider  a  little  more  fully  the  subject 
of  motion,  and  particularly  that  of  bodies  moving  under 
the  action  of  forces. 

Motions  may  vary  as  to  their  velocity,  and  these 
differences  may  be  expressed  by  numerical  or  other 
symbols.  The  idea  of  velocity  involves  the  ideas  of 
time  and  length  and  direction — as  we  speak  of  a  body 
moving  in  a  given  direction  at  the  rate  of  "  ten  miles 
an  hour,"  and  the  unit  of  velocity  can  be  defined 
only  by  reference  to  the  unit  of  length  and  the  unit  of 
time. 

"  Velocity "  is  sometimes  called  the  "  intensity  of 
motion,"  but  the  quantity  of  the  motion  of  any  body, 
which  is  called  its  "  momentum,"  is  very  different 
from  its  velocity,  and  refers  jointly  to  the  amount  of 
matter  of  which  a  moving  body  consists  as  well  as 
to  its  velocity.  Thus  if  two  bodies  are  moving  with  equal 
velocity,  the  quantity  of  motion  in  each  corresponds 
with  -its  mass,  and  if  two  bodies  of  equal  mass  are  in 


MECHANICS  55 

motion  the  quantity  of  motion  in  each  will  then  be 
proportional  to  its  velocity. 

If  two  unequal  bodies  are  moving  with  different 
velocities,  their  quantity  of  motion  is  jointly  proportional 
to  their  respective  masses  and  velocities. 

But  motions  may  not  be  of  uniform  velocity  during  the 
time  they  last ;  they  may  be  continually  accelerated  or 
retarded,  so  that  their  velocity  varies  from  moment 
to  moment  owing  to  some  accelerating  or  retarding 
cause. 

Matter  itself  must  be  regarded  as  absolutely  inert — 
not  inert,  however,  in  the  sense  that  it  is  more  inclined 
to  rest  than  to  motion,  or  that  motion  naturally  tends 
to  come  to  an  end.  By  calling  motion  "inert,"  it  is 
simply  meant  that  matter  is  totally  indifferent  to  either 
rest  or  motion,  and  therefore  it  has  been  purposed 
to  speak  of  this  quality  as  persistence  rather  than 
inertia. 

The  following  are  Newton's  three  laws  of  motion : 

(i)  Every  body  continues  in  its  state  of  rest,  or  of 
motion  in  a  straight  line,  except  in  so  far  as  it  is  compelled 
by  impressed  foi'ces  to  change  that  state. 

Now  there  is  no  such  thing  as  absolute  rest,  since, 
as  we  have  seen,  every  body  tends  to  move  in  the  direc- 
tion in  which  gravity  draws  it,  and  only  does  not  so  move 
because  some  other  force  prevents  it.  Therefore  what 
the  first  part  of  this  law  really  asserts  is,  that  when  a 
body  is  maintained  in  a  certain  state  and  position  by 
the  combined  action  of  two  or  more  forces,  such  state 
will  continue  till  some  other  force  changes  the  con- 
ditions. 

The  second  part  of  the  law  affirms  that  a  body  in 
motion  tends  to  move  uniformly  in  a  straight  line.  This 
necessarily  means  that  its  movement  must  continue  in 


56  ELEMENTS   OF   SCIENCE 

the  same  direction,  until  some  other  force  changes  that 
direction. 

(2)  Change  of  motion  is  proportional  to  the  impressed 
force,  and  takes  place  along  the  straight  line  in  which  that 
force  is  impressed. 

This  means  that  whatever  motion  (and  by  motion  is 
here  meant  quantity  of  motion)  any  force  produces,  twice 
or  three  times  such  force,  or  such  force  acting  for  twice 
or  three  times  the  duration,  will  produce  twice  or  three 
times  as  much  motion,  and  so  on. 

Therefore  when  several  forces  act  together,  the  change 
of  action  due  to  each  is  proportional  to  each,  and  their 
combined  effect  must  be  the  same  as  if  each  had  acted 
separately  or  successively.  Any  body  simultaneously 
acted  on  by  two  or  more  forces  will  be  carried  to  the  spot 
it  would  eventually  have  reached  had  the  same  forces 
acted  separately  and  successively. 

(3)  To   every  action  there   is   an  equal  and   opposite 
reaction;   as   the  mutual  actions  of  two  bodies  on   one 
another  are  always  equal  and  in  opposite  directions. 

In  other  words :  any  body  set  in  motion  by  another 
body  will  react  upon  the  latter  in  an  opposite  direction, 
and  the  second  body  will  lose  a  quantity  of  motion 
exactly  equal  to  that  which  the  first  received. 

Thus  if  any  body  A,  exerts  a  force  on  another  body  B, 
B  must  also  exert  on  A  an  equal  force  in  an  opposite 
direction. 

Thus  every  force  is,  in  fact,  one  of  a  pair  of  forces,  and 
such  a  pair  of  forces  is  called  a  stress.  We  have  an  ex- 
ample of  a  pair  of  forces  of  the  kind  in  those  which  lead 
a  body  revolving  in  a  circle,  respectively  to  approach  and 
to  fly  away  from  that  circle's  centre.  These  two  forces 
are  respectively  known  as  "centrifugal"  and  "centri- 
petal "  forces. 


MECHANICS  57 

Here,  as  before,  when  dealing  with  geometry,*  what 
we  see  in  real  life  does  not  exactly  correspond  with 
abstract  scientific  principles.  All  the  motions  we  ob- 
serve about  us  sooner  or  later  come  to  an  end,  and  no 
body  propelled  from  the  earth's  surface  goes  on  long 
in  one  direction,  but  sooner  or  later  descends  to 
the  earth.  These  facts  are,  of  course,  due  to  friction 
which,  in  different  degrees,  retards  motion,  and  to  the 
force  of  gravity  which  draws  all  things  that  may  be 
propelled  from  the  earth's  surface  downwards  again 
towards  its  centre.  Therefore  in  many  dynamical 
problems  we  have  to  neglect  the  consideration  of 
friction.  But  friction  may  not  only  be  more  or  less 
diminished,  it  may  be  actually  neutralised  by  the  action 
of  some  other  force. 

Thus  a  railway  train  once  set  in  motion  would, 
according  to  our  first  law  of  motion,  continue  onwards 
uniformly  if  its  motions  were  not  retarded  by  any 
other  force;  but  friction  tends  to  prevent  this,  and  it 
would  soon  stop  the  train  but  that  the  force  generated 
by  the  engine  is  sufficient  to  overcome  the  impeding 
influence  of  friction.  The  train  will  thus  continue 
onwards  in  uniform  motion  under  the  influence  of 
opposing  forces. 

The  motions  which  pertain  to  any  separate  body,  con- 
tinue unaffected  by  a  motion  common  to  it  and  other 
bodies  also — e.g.,  a  watch  will  continue  its  proper  move- 
ments while  in  the  pocket  of  a  man  running  a  race. 
This  truth  is  connected  with  the  second  law  of  motion, 
which  affirms  the  effective  independent  action  of  forces 
apparently  combined. 

It   may   be   illustrated    by   the   fact    that   a  weight 

*  See  ante,  p.  36. 


ELEMENTS   OF   SCIENCE 


FIG.  n. 


dropped  from  the  top  of  the  mast  of  a  ship  in  rapid 
motion  will  fall  on  the  same  spot  as  it  would  do 
were  the  ship  at  anchor.  For  it  participates  in  the 
onward  motion  of  the  ship,  and  this  horizontal  im- 
pulse prevents  its  being  left  behind  by  the  motion  of 
the  ship  during  the  time  of  its  descent. 

It  may  also  be  illus- 
trated by  the  impulse 
given  by  a  billiard  cue 
to  a  ball  B,  by  caus- 
ing ifc  to  strike  against 
the  cushion  of  a  bil- 
liard table  at  the  point 
X  (Fig.  n).  As  we 
have  seen,  this  force, 
represented  by  the  line 
X  from  a  to  X,  may  be 
resolved  into  two  forces 
represented  by  a  b  and 
a  c.  Their  combined 
action  (represented  by 
the  diagonal  aX.)  would 
bring  the  ball  to  the 
point  X.  There  the 
force  Xc  would,  by 
the  third  law  of  motion,  cause  a  reaction  by  the 
cushion  on  the  ball,  tending  to  drive  it  back  along  the 
parallel  line  Xc.  For  only  the  force  db  has  acted  on 
the  cushion,  while  the  force  ac  has  met  with  no  resist- 
ance. This  last  force,  then,  is  still  in  full  operation, 
and  acting  together  on  the  impulse  Xc,  carries  the  ball 
to  the  position  d.  On  comparing  the  diagonal  BX  with 
the  diagonal  Xc?  we  see  that  the  angle  BXc  equals 
the  angle  cXd,  or,  in  other  words,  that  "  the  angle  of 


MECHANICS  59 

reflexion  equals  the  angle  of  incidence  " — a  truth  of  the 
greatest  value  to  billiard  players  though  they  have  to 
allow  for  the  friction  and  other  conditions  which  prevent 
this  equality  being  attained  on  any  billiard  table  with 
absolute  exactness. 

When  a  body  is  once  in  motion,  force  is  not  needed 
to  maintain  the  motion.  When,  however,  there  is  any 
change  in  the  direction  or  speed  of  a  moving  body,  then 
we  have  evidence  of  the  existence  of  force.  This  is  only 
another  way  of  stating  the  first  law  of  motion. 

Therefore  any  continued  force  must  produce  a  con- 
tinuous change,  either  in  direction  or  velocity.  A  sudden 
change  of  either  kind  is  produced  by  impact,  i.e.,  by  an 
instantaneous  exertion  of  force. 

From  what  we  saw  with  respect  to  quantity*  of 
motion,  it  may  be  approximately  deduced  that  a  charge  of 
gunpowder  which  would  impart  to  a  bullet  of  a  certain 
size  a  velocity  which  we  may  express  by  100,  would 
impart  to  a  bullet  ten  times  that  size  only  a  velocity 
of  10. 

Various  interesting  apparatuses  have  been  invented 
to  illustrate  these  laws  of  motion,  but  for  their 
description  and  a  vast  mass  of  further  information,  the 
reader  must  have  recourse  to  distinct  treatises  on 
dynamics. 

When  a  force  acts  continuously  upon  a  body,  the 
effect  is  necessarily  cumulative,  and  in  that  case  its 
velocity  will  be  constantly  quickened  and  accelerated. 
If  we  let  fall  from  our  hands  at  the  same  time  a 
feather  and  a  marble,  the  latter  falls  at  once  very 
quickly  to  the  ground,  while  the  other  falls  very  slowly 
and  with  many  oscillations. 

*  See  ante,  p.  54. 


60  ELEMENTS   OF   SCIENCE 

The  reader  will  at  once  understand  that  it  is  only 
the  resistance  of  the  air  which  prolongs  the  feather's 
descent.  Accordingly,  if  they  are  made  to  fall  in  the 
nearest  approach  to  a  vacuum  which  an  air-pump  can 
produce,  they  will  fall  simultaneously. 

If  a  bullet  be  taken  in  the  right  hand  and  be  allowed 
to  fall  thence  into  the  left  hand  through  a  height  of  a 
few  inches,  it  will  give  a  slight  blow.  If  it  be  allowed 
to  fall  a  yard,  it  will  be  felt  more  smartly,  while  if  it 
were  to  descend  on  the  hand  from  a  second-floor  window 
the  blow  would  be  severe. 

Therefore  the  longer  a  fall  lasts — the  greater  the 
distance  through  which  a  body  falk — the  greater  is 
its  energy  and  the  greater  the  rapidity  of  its  motion. 
The  motion  of  a  falling  body  is  a  uniformly  accelerated 
motion,  because,  the  attraction  between  the  earth 
and  the  body  never  ceasing  to  act,  the  body  gains  a 
fresh  momentum  every  instant.  Therefore  it  falls 
to  the  ground  with  a  velocity  which  is  the  aggre- 
gate of  all  the  indefinitely  small  but  equal  increments 
of  velocity  thus  communicated  to  it. 

Now  it  has  been  discovered  that  a  falling  body 
acquires,  at  the  end  of  the  first  second  of  its  fall,  a 
velocity  of  about  32.2  feet  a  second — i.e.,  a  velocity 
which  would,  alone,  carry  it  through,  say,  32  feet 
during  the  second  second.  During  this  second,  how- 
ever, it  will  have  fallen  through  only  16  feet.  During 
the  second  second  it  will  fall  through  the  32  feet  (from 
the  velocity  with  which  it  starts)  and  through  16 
additional  feet  on  account  of  the  constant  action  of 
the  force  of  gravity.  Similarly,  it  will  fall  64  feet 
during  the  third  second  plus  16  feet,  and  so  on,  as 
shown  by  the  following  table  wherein  the  time  of 
each  second  is  represented  by  a  similar  length,  vejo* 


MECHANICS 


61 


city    by   breadth,   and   the   distance   fallen    by   extent 
of  area  : 

FIG.  12. 


Starting  with  a  velocity  of 

Falling  during  ist  second 
Velocity  acquired  at  end  ) 
of  ist  second      .       .  j 

Falling  in  2nd  second 
Velocity  at  its  end  2  x  32  . 

Falling  during  3rd  second 
Velocity  acquired  at  end  ) 
of  3rd  second  3X32   .} 

Falling  during  4th  second 
Velocity  acquired  at  end  ) 
of  4th  second  4  x  32    .  } 

I 

if, 

, 

16\ 

.  per  second. 

48 

k    64  ft.  per  second. 

\8o 

32+ 

32+ 

32+ 

•     oc 

32+ 

32+ 

32+  16\ 

And  falling  a  total  distance  of  4  times  4  times  1 6ft.  =    .  .  2j6 

But  though  a  body  falls  16  feet  in  a  second,  it  will 
only  fall  4  feet  in  half  a  second,  for  it  is  then  falling  at 
only  half  its  speed  per  second.  Thus,  as  Galileo  observed, 
the  distance  fallen  is  proportional  to  the  square  of  the 
time  occupied  by  it. 

Thus  if  we  know  the  time  which  has  been  occupied  by 
a  fall,  we  can  determine  the  space  through  which  it  has 
fallen  by  multiplying  the  square  of  the  time  by  the 
number  of  feet  through  which  a  body  falls  in  one 
second. 


During  one  second  it  will  have  fallen  i  x  16  ft.  =    16  ft. 
„      two  seconds,,     „       „         „      4Xi6,,=    64    „ 

"         »       9  x  l6  3J  =  144    „ 


three 
four 


16  x  16  „  =256 


62  ELEMENTS   OF   SCIENCE 

It  also  follows  from  the  foregoing  facts  that  the  velo 
city  a  body  acquires  in  falling,  is  as  the  square  root  of  the 
height  fallen  through.  Thus,  to  acquire  a  velocity  of 
32  feet  per  second  it  must  fall  a  distance  of  42  feet ;  for 
a  velocity  of  64  feet  per  second,  48  feet ;  and  for  96  feet 
per  second,  80  feet  and  so  on.  The  distances  fallen 
through  during  equal  successive  intervals  are  as  the 
series  of  odd  numbers  i,  3,  5,  7,  &c. 

These  laws  apply  not  only  to  the  motion  of  Jailing  but 
also  to  all  uniformly  accelerated  motions  ;  only  the  rate 
of  acceleration  is  never  so  rapid  on  inclined  planes  or  in 
any  other  conditions,  as  when  falling  freely.  All  freely 
falling  bodies  are  accelerated  at  the  same  rate,  because 
however  they  may  differ  in  mass,  the  force  of  gravity 
acts  on  them  in  exact  proportion  thereto — acting  twelve 
times  more  forcibly  on  a  mass  of  twelve  pounds,  than  on 
a  mass  of  one  pound. 

The  pendulum,  while  one  of  the  simplest  of  scientific 
instruments,  is  also  one  of  the  most  valuable.  If  a 
small,  heavy  body  be  suspended  by  a  thread  from  a  fixed 
point,  that  will  form  an  instrument  of  the  kind  of  a  most 
simple  description. 

When  at  rest,  the  line  from  the  point  of  suspension  S 
(Fig.  13),  to  the  weight  A,  serves  to  indicate  the  line  along 
which  gravity  acts — the  "plumb-line"  or  vertical  line. 

When  the  weight  is  drawn  on  one  side,  and  then  let 
go— e.g.,  if  A  be  drawn  to  C  and  then  allowed  to 
fall  in  a  vertical  plane — it  will,  after  descending  to  its 
former  position,  ascend  on  the  other  side  as  far  as  B — 
that  is,  nearly  as  far  from  A  on  one  side  as  C  was  on 
the  other.  It  will  then  descend  again  and  afterwards 
ascend  nearly  as  high  as  was  the  point  B,  and  so  on. 
Its  entire  sweep  from  C  to  B  is  called  one  vibration, 
or  oscillation  of  the  pendulum,  and  its  extent  or  anipli- 


MECHANICS 


FIG.  13. 

n 
S 


tude  is  measured  by  degrees,  minutes,  and  seconds  of 
an  arc  which  may  be  placed  so  as  to  measure  it.  360 
.degrees  have  been  adopted  as  subdivisions  of  a  circle, 
each  such  "degree"  being  subdivided  into  60  minutes 
and  each  such  minute  into  60  seconds. 

The  time  occupied  by  a  pendulum  in  one  oscillation 
constitutes  the  duration  of  a  vibration.  Were  it  not 
for  friction  and  the  re- 
sistance of  the  air,  the 
weight  would  ascend  al- 
ways to  the  same  height 
on  either  side  as  that 
whence  it  first  started, 
and  so  would  constitute 
an  instrument  with  per- 
petual motion,  since  the 
action  of  the  force  of 
gravity  is  incessant. 
Within  certain  limits, 
the  time  occupied  by  a 
vibration  is  not  altered 
by  increasing  its  ampli- 
tude, because  the  more 
the  weight  be  elevated, 
the  more  the  speed  of 
its  descent  will  be  increased,  and  in  exact  proportion  to 
the  degree  of  elevation. 

The  vibration  of  pendulums  being  thus  a  simple  and 
direct  effect  of  the  force  of  gravity,  they  have  been  made 
use  of  to  measure  variations  in  that  force  at  different 
places,  to  estimate  the  density  of  matter  beneath  the 
surface  of  the  ground,  and  even  to  determine  the  shape 
of  the  earth. 

It  has  been  ascertained  that  the  time  occupied  by  a 


10 


64  ELEMENTS   OF   SCIENCE 

pendulum  in  its  oscillation,  varies  as  the  square  root  of 
its  length,  thus  four  pendulums,  the  relative  lengths  of 
which  may  be  represented  by  the  numbers  i,  4,  9,  and 
1 6,  will  oscillate  in  periods  represented  by  i,  2,  3, 
and  4. 

All  that  has  been  said  with  respect  to  uniformly 
accelerated  motion  applies  equally  to  uniformly  retarded 
motion.  Thus  when  any  body  is  projected  straight 
upwards  from  the  earth's  surface,  it  rises  32  feet  less 
during  each  succeeding  second,  till  its  velocity  (which  is 
decreased  during  the  ascent  as  it  increases  during  a 
descent)  is  exhausted.  Thus  it  must  pass  each  successive 
point  as  it  descends  again,  with  the  same  velocity  as  that 
it  possessed  as  it  passed  each  such  point  during  its 
ascent. 

But  we  have  constantly  to  consider  the  joint  effects 
of  a  body  with  uniform  motion  and  a  uniformly  accele- 
rated motion — as,  for  example,  when  a  shot  is  fired 
from  a  cannon.  Such  a  body  is  impressed  with  the 
uniform  motion  imparted  by  the  explosion  and  with  the 
uniformly  accelerated  motion  due  to  the  force  of  gravity. 
Putting  entirely  aside  the  action  of  friction  and  atmo- 
spheric resistance,  we  find  that  there  is  an  exact  compo- 
sition of  forces.  Thus  at  any  moment  the  cannon  ball 
will  be  at  the  spot  it  would  have  reached  had  it  been 
carried,  in  a  straight  line,  to  the  elevation  it  would  have 
attained  by  the  force  of  projection  acting  alone,  during 
the  time  elapsed,  and  then  fallen  thence  in  an  exactly 
similar  time.  The  junction  of  all  these  points  of  coinci- 
dence— i.e.,  the  path  followed  by  the  projectile  always 
forms  a  peculiar  curved  line  called  a  parabola — a  curve 
such  as  would  be  produced  by  the  margin  of  a  section  of 
a  circular  cone  cut  through  parallel  to  any  part  of  its 
slanting  surface. 


MECHANICS  65 

Another,  and  a  most  noteworthy,  conic  section* 
is  one  formed  by  cutting  across  a  cone  in  any  place, 
not  at  right  angles  to  its  base.  It  may  be  drawn 
in  the  following  simple  way :  If  two  ends  of  a  thread 
be  attached  to  two  points  of  a  horizontal  surface — 
the  thread  being  much  longer  than  the  distance 
between  such  two  points — and  if  a  pencil  be  so  placed 
as  to  stretch  the  thread  outwards  as  much  as  pos- 
sible, and  then  be  carried  round  (always  so  stretching 
the  thread)  till  it  describes  a  closed  curve,  such  a  figure 
will  be  an  ellipse.  The  two  points  of  attachment  of  the 
thread,  form  what  are  called  the  Joci  of  the  ellipse,  and 
the  more  these  are  approximated  the  more  circular  the 
ellipse  will  become ;  and  it  becomes  transformed  into  a 
circle  as  soon  as  they  coincide. 

Now  if  a  body  were  projected  horizontally  from  a 
point  external  to  the  earth's  surface  with  sufficient 
velocity,  it  would  be  carried  in  a  certain  time  to  a  much 
greater  distance  than  gravity  would  make  it  fall  during 
that  same  time,  and  then  (if  there  were  no  air)  it  would 
never  fall  to  that  surface,  but  would  continually  go 
round  the  earth  in  an  ellipse — the  precise  form  of  which 
would  depend  on  the  exact  velocity  and  direction  given 
to  the  body. 

Every  stone  flung  into  the  air  describes  a  little  bit 
of  an  ellipse  round  the  centre  of  the  earth,  which  it 
would  complete  but  for  the  overpowering  attraction 
of  the  earth. 

It  has  been  ascertained  that  such  a  body,  whatever 
the  amount  of  its  divergence  from  a  circle — i.e.,  what- 
ever the  eccentricity  of  the  ellipse  in  which   it  migh 
move — would  be  subject  to  the  following  law  : 

*  See  ante,  p.  37. 


66  ELEMENTS    OF   SCIENCE 

A  line  drawn  from  it  to  the  centre  of  the  earth,  must 
always  move  in  the  same  plane,  and  in  such  a  way  as  to 
pass  over  equal  areas  in  equal  times.  Such  a  line  is 
called  a  "  radius  vector" 

But  the  force  of  gravity  between  bodies  does  not  alone 
draw  everything  at  or  near  the  earth's  surface,  towards 
the  earth's  centre,  it  also  draws  every  existing  body 
towards  every  other,  although  its  action  between  small 
bodies  is  too  feeble  to  be  easily  observed. 

Each  body  thus  draws  towards  itself  every  other  body 
with  a  force  of  gravity  which  varies  directly  as  its  mass 
and  inversely  as  the  square  of  its  distance  from  the  body 
it  attracts. 

On  account  of  the  inertia  of  matter,  or  its  absolute 
indifference  to  motion,  every  separate  body  on  the  earth's 
surface  would,  by  the  force  of  the  earth's  rotation,  be 
projected  a.nd  continue  on  ward  i  in  a  straight  line  from 
its  surface — in  a  tangent* — were  it  not  for  the  force  of 
gravity  which  keeps  it  in  its  place.  The  passive  tendency 
to  continue  onwards  in  a  tangential  straight  line — or 
"  to  fly  oft'" — is,  as  before  said,  termed  "centrifugal 
force,"  while  the  action  of  gravity  which  conflicts  there- 
with is  called  "centripetal  force."  These  two  forces 
arise  together,  and  illustrate  that  bifold  nature  of  forces 
implied  in  Newton's  third  law.f 

Now,  as  we  all  know,  the  earth  revolves  on  its  axis 
once  in  every  twenty-four  hours. 

The  weight  of  any  object,  then,  is  that  portion  of  its 
gravity  over  and  above  that  which  is  required  to  prevent 
its  "flying  off"  (owing  to  our  globe's  rotation),  and  to 
retain  it  on  the  earth's  surface.  Had  bodies  no  more 

*  A  tangent  is  a  line  touching  the  circumference  of  a  circle 
and  at  right  angles  to  the  diameter  of  the  circle  at  tLe  point 
of  contact.  t  See  ante,  p.  56. 


MECHANICS  67 

gravity  than  would  be  required  to  effect  this,  they 
would  have  absolutely  no  weight  and  would  exercise  no 
pressure  whatever.  It  is  the  tendency  to  "  fly  off"  from 
a  horse's  back  produced  by  rapidly  riding  in  a  circle, 
which  so  reduces  the  weight  of  a  circus  rider  that  he 
can  easily  stand  on  the  saddle  and  perform  a  number  of 
feats  any  one  of  which  would  be  impossible  did  he  ride 
in  a  straight  line. 

On  account  of  the  greater  rapidity  of  motion  of  the 
earth's  surface  towards  the  equator  than  towards  the 
poles,  the  centrifugal  force  is  necessarily  greater  at 
the  equator,  and  consequently  weight  is  there  slightly 
diminished,  as  is  easily  proved  by  the  vibrations  of  a 
pendulum.  On  account  also  of  the  greater  mass  of  the 
earth's  equatorial  region,  a  plumb  line  does  not,  in  the 
north,  hang  absolutely  vertical  to  the  earth's  surface, 
but  deviates  slightly  to  the  south. 

With  these  various  elementary  observations  we  must 
conclude  what  we  have  to  say  respecting  the  mechanics 
of  solid  bodies,  referring  the  student  to  other  works  for 
the  prosecution  of  his  study  of  that  science. 

Passing  on  now  to  the  consideration  of  fluid  substances, 
we  may  first  remark  that  the  essential  principles  of 
dynamics,  apply  to  them  as  well  as  to  solids,  but  the 
fluid  condition  calls  forth  new  conceptions,  which  are 
treated  of  as  distinct  sciences  known  as  hydrostatics, 
hydrodynamics,  and  pneumatics. 

All  fluids,  whether  liquid  or  aeriform,  are,  of  course, 
no  less  subject  to  the  action  of  gravity  than  are  solids, 
but  the  commonest  observation  makes  it  clear  that  the 
internal  constitution  of  their  substance  must  somehow  be 
very  different  from  that  of  solids.  In  what  precisely  that 
difference  consists  we  do  not  know,  though  any  specula- 
tions are  useful,  provided  that  (as  working  hypotheses) 


68  ELEMENTS   OF  SCIENCE 

they  serve  to  help  us  on  to  a  better  knowledge  of  the 
laws  which  govern  fluid  bodies. 

As  to  liquids,  we  may  assume  them  to  be  made  up 
of  particles,  which,  instead  of  cohering  stably  in  some 
definite  order  (as  we  assume  to  be  the  case  with  the  par- 
ticles of  solid  bodies),  have  no  tendency  to  preserve  any 
reciprocal  positions,  but  can  move  and  glide  over  each 
other  with  perfect  freedom  and  in  all  directions,  each  par- 
ticle pressing  equally  on  all  the  particles  which  surround 
it  and  being  equally  pressed  on  by  them. 

By  this  hypothesis  we  may  understand  the  great 
difference  which  exists  between  a  liquid  and  a  solid. 
Hitherto  our  conception  of  pressure  due  to  weight,  has 
been  simply  downwards,  through  the  force  of  gravity. 
But  a  portion  of  liquid  presses  equally  in  all  directions, 
in  consequence  of  the  action  of  gravity,  or  of  any  other 
force  acting  upon  it. 

Therefore  for  liquid  to  be  in  equilibrium,  every  particle 
of  it  must  press  and  be  pressed  upon  equally  in  all  direc- 
tions. One  consequence  of  this  is  that  the  surface  of  a 
liquid,  apart  from  any  disturbing  influence,  must  be 
horizontal.  An  illustration  of  the  imagined  condition  of 
liquids,  may  be  obtained  by  considering  the  consequences 
which  would  be  produced  should  a  fresh  comer  try  to 
effect  an  entrance  into  a  room  already  filled  by  a  crowd 
of  persons,  The  new  comer  who  manages  to  effect  such 
an  entrance  will  produce  pressure  in  all  directions — on 
every  side  of  him. 

From  the  mobility  of  its  particles  it  follows  that  a 
liquid  immediately  takes  the  figure  of  any  vessel  in 
which  it  may  be  received.  Therefore,  if  two  or  more 
vessels,  however  different  their  sizes,  which  contain  liquid 
of  the  same  kind,  be  placed  in  communication  (e.g.,  by 
turning  stop-cocks)  below  the  surface  of  the  liquid  in  any 


MECHANICS 


one  of  them  the  fluid  in  the  whole  of  them  will  settle 
itself  at  one  and  the  same  level,  or,  as  is  commonly  said, 
"  water  will  always  find  its  own  level." 

It  has  been  said  that  liquids  transmit  pressure,  not 
only  in  the  direction  opposite  to  that  in  which  it  is 
applied,  but  equally  in  all  directions;  thus  a  hollow 
vessel  may  be  filled  with  water,  which  it  will  hold  quite 
securely.  But  if  a  long  tube  be  screwed  into  the  top  of 
it  and  filled  with  water,  it  will  cause  the  so-filled  vessel 
to  burst,  if  the  tube  and  column  of  water  be  sufficiently 

FIG.  14. 


ii  q?    ir    e 


high  ;  and  it  makes  no  difference  whether  the  tube  be 
stout  or  slender. 

Therefore  the  weight  of  even  half  an  ounce  of  water 
will  burst  any  vessel,  if  the  tube  and  column  of  water 
are  only  high  enough ;  for  on  account  of  the  equality  of 
pressure  in  all  directions,  a  pressure  equal  to  the  whole 
weight  of  the  entire  column  will  be  exerted  on  every 
part  of  the  inner  surface  of  the  hollow  vessel,  which  is 
of  equal  size  with  the  bore  .of  the  elongated  tube. 

In  hydrostatics,  it  is  assumed  that  liquid  bodies 
are  practically  incompressible.  Such  is  not  actually  the 
case,  though  pressure  will  only  reduce  their  bulk  so  in- 
considerably that  the  result  of  such  action  may  practi- 
cally be  disregarded. 

The  pressure  of  water  of  the  height  of  one  foot  is 


70  ELEMENTS   OF   SCIENCE 

about  half  a  pound  for  the  square  inch;  and  as  we 
increase  the  height  a  foot,  the  pressure  increases  half 
a  pound.  In  a  cubical  vessel  the  pressure  of  a  liquid 
filling  it  is,  as  before  said,  equal  on  all  sides,  and  its 
pressure  on  each  side  is  equal  to  half  the  weight  of  the 
liquid.  Therefore  a  liquid  in  a  cube  exercises,  on  base 
and  sides,  three  times  as  much  pressure  as  that  pro- 
duced by  its  weight  alone.  Let  us  suppose  its  weight 
exercises  a  pressure  of  one  pound,  then  the  pressure 
exercised  on  each  side  of  the  cube  will  be  half  a  pound — 
that  is,  a  pressure  of  two  pounds,  besides  the  pressure, 
due  to  gravity,  of  one  pound  on  the  base  of  the  cube. 

Any  solid  body  immersed  in  a  liquid,  necessarily  dis- 
places a  quantity  of  that  liquid  exactly  equal  to  its  own 
bulk.  If  it  also  exactly  equals  this  displaced  quantity 
in  weight,  it  will  remain  indifferently  at  any  depth  in 
the  liquid  without  any  tendency  to  rise  or  sink.  If  its 
weight  is  greater  it  will  of  course  sink,  and  if  less,  it 
will  rise.  Not  that,  of  course,  it  has  any  spontaneous 
tendency  in  itself  to  rise ;  it  simply  rises  because  the 
greater  pressure  pushes  it  upwards.  But  a  body  which 
sinks,  apparently  loses  just  as  much  of  its  own  weight 
as  the  water  it  displaces  weighs,  as  may  easily  be  ascer- 
tained experimentally. 

Since  liquids  press  equally  in  all  directions,  any 
object  immersed  in  them  must  be  at  least  as  much 
pressed  upwards  by  pressure  from  below,  as  it  is 
depressed  by  pressure  from  above.  Thus  fishes  can 
swim  with  ease  at  depths  where  they  must  be  sub- 
jected to  enormous  pressure  from  above,  since  they  are 
sustained  by  a  somewhat  greater  pressure  from  below. 

If  a  solid  body  be  first  weighed  in  air  and  then  in 
water ;  if  its  weight  in  the  latter  be  subtracted  from  its 
weight  in  the  former  and  its  weight  in  air  be  divided  by 


MECHANICS  71 

the  difference,  the  product  will  be  what  is  called  the 
specific  gravity  of  that  solid.  Let  us  suppose  a  solid 
weighs  75  grains  in  water,  and  80  in  air;  then  80  -  75  =  5 

and  —  —  1 6.   The  proportion,  therefore,  of  the  weights  of 

equal  bulks  of  the  solid  in  question  and  of  water,  will  be 
80  to  5  or  1 6  to  r,  so  that  it  will  be  16  times  heavier 
than  its  own  bulk  of  water,  and  the  specific  gravity  of 
that  body  will  be  16. 

In  England  it  is  customary,  for  convenience,  to  con- 
sider one  cubic  foot  as  the  standard  volume,  and  to  ex- 
press the  weight  in  avoirdupois  ounces  or  grains,  and  a 
cubic  foot  of  rain-water  weighs  about  1,000  oz.  The 
specific  gravities  of  liquids  may  be  ascertained  by  using 
a  vessel  capable  of  holding  1000  grains  of  water  at  a 
temperature  of  60°  Fahrenheit. 

If  two  liquids  which  differ  in  density — such  as  water 
and  alcohol,  or  water  and  mercury— be  made  to  com- 
municate in  a  vessel  with  two  upward  prolongations,  or 
limbs,  then  the  height  to  which  they  will  rise  in  the  two 
limbs  will  differ  inversely  as  their  densities — the  more 
dense  being  the  less  high.*  Thus  two  inches  of  mer- 
cury will  balance  27  inches  of  water. 

We  have  said  t  that  the  surface  of  a  liquid  is  hori- 
zontal, "apart  from  any  disturbing  influence";  but 
certain  attractions,  other  than  the  earth's  gravity, 
may  interfere,  more  or  less,  with  the  horizontality  of  a 
fluid's  surface. 

Thus  there  is,  of  course,  an  attraction  between  the 
vessel  holding  a  liquid  and  the  adjacent  portion  of  such 
liquid.  If  the  solid  vessel  be  denser  than  the  liquid 

*  As  to  "  osmosis,"  another  effect,  of  placing  in  proximity, 
p.  146.  t  See  «»'«»  P-  68. 


72  ELEMENTS    OF   SCIENCE 

(as  in  the  case  of  water  in  a  glass  vessel)  then  the  surface 
of  the  liquid  will  rise  at  its  circumference  so  that  its 
upper  surface  is  concave.  If  the  liquid  be  much  denser 
than  the  vessel  containing  it  (as  with  mercury  contained 
in  glass),  then  the  surface  of  the  liquid  will  be  slightly 
depressed  at  its  circumference  and  the  upper  surface  of 
the  mercury  will  therefore  be  convex. 

This  attraction,  which  is  due  to  the  surface  contact  of 
the  liquid  and  solid,  is  shown  on  plunging  any  solid  body 
into  water,  when  some  of  the  water  adheres  to  it  and  comes 
out  wet.  If  thin  plates  of  different  substances  be  made  to 
touch  the  surface  of  water,  considerable  force  is  required 
to  raise  them  from  it,  and  the  amount  of  force  thus 
required  varies  in  amount  with  the  nature  of  the  sub- 
stance employed.  One  conspicuous  form  of  such  action 
is  that  which  is  known  as  capillary  attraction.  This  is 
the  attraction  exercised  by  tubes  of  very  fine  bore  upon 
liquids  into  which  their  ends  may  be  plunged. 

If  any  substance  containing  minute  canals  of  the  kind, 
be  immersed  in  water,  then  the  water  will  ascend  them 
to  a  height  which  will  be  the  greater  the  narrower  the 
cavities  it  ascends.  As  examples  of  such  action  may  be 
taken  the  small  cavities  in  blotting  paper,  sponge,  the 
cotton  of  a  lamp,  lump  sugar,  &c.,  in  all  of  which  liquid 
will  readily  ascend.  It  is  because  such  cavities  are 
generally  not  broader  than  a  human  hair  that  this 
attraction  has  been  termed  "  capillary." 

The  motions  of  liquids  constitute  another  section  of 
mechanics  known  as  hydrodynamics  or  hydraulics. 
Since  liquids  can  be  set  in  motion  with  so  much  greater 
facility  than  solids,  and  since  the  direction  and  velocity 
of  their  movements  are  liable  to  modification  by  so 
many  causes  which  would  not  modify  the  action  of  mov- 
ing solids,  it  is  evident  that  the  conditions  of  their 


MECHANICS  73 

movements  must  be  relatively  complex.  Nevertheless 
the  motions  of  liquids  have  the  same  basis  and  obey  the 
fundamental  laws  of  the  movements  of  solid  bodies. 

We  have  seen  that,  abstracting  the  action  of  the 
atmosphere,  all  bodies  which  fall  from  the  same  height 
fall  simultaneously  and  attain  the  same  velocity  at  each 
stage  of  their  descent.  We  have  also  seen*  that  the 
velocities  they  require  are  as  the  square  roots  of  the 
heights  through  which  they  fall,  so  that  an  object  must 
be  four  times  higher  than  another  if  we  desire  that  it 
should  attain  twice  the  velocity  of  the  latter. 

Let  us  suppose  that  we  have  two  vessels  before  us,  each 
containing  a  depth  of  four  feet  of  water,  but  that 
one  vessel  is  six  feet  in  diameter,  while  the  other  has 
but  a  breadth  of  one  foot.  Further  let  us  suppose 
that  a  similarly  sized  hole  be  made  in  each  vessel 
six  inches  from  the  bottom.  It  might  be  thought 
that  the  stream  issuing  forth  from  the  larger  vessel 
will  be  projected  much  further  than  that  from  the 
smaller  one.  Such,  however,  is  not  the  fact ;  they 
will  be  projected  equally  far.  Not  only  is  this  the 
case,  but  it  will  be  the  same  if  the  two  liquids  are  of 
different  densities.  Mercury  will  be  projected  as  far, 
and  no  further  than,  water,  if  they  both  issue  from 
similar  orifices,  placed  at  the  same  depth  beneath  the 
surfaces  of  the  two  liquids.  Here,  as  -with  solids,  if  we 
wish  to  double  the  velocity  we  must  raise  the  surface  of 
the  fluid  fourfold,  and  to  make  it  four  times  as  great 
we  must  raise  it  sixteenfold  and  so  on  •  and  the  greater 
the  velocity,  the  further  outwards  will  the  jet  of 
discharge  extend.  This  jet,  in  falling,  always  describes 
a  parabola,  i.e.,  falls  in  a  parabolic  curve.  The  particles 

*  See  ante,  p.  60, 


74  ELEMENTS   OF   SCIENCE 

of  water,  in  issuing  from  an  orifice  of  a  vessel  (at  the 
bottom),  do  not,  as  Newton  has  shown,  pass  perpendicu- 
larly to  and  through  ifc.  Many  of  them  converge  towards 
it  from  every  side  •  so  that  after  passing  out  of  the  orifice 
they  form  a  stream  of  diminished  breadth,  which  he 
called  the  Vena  contracta.  As  the  liquid  issues  forth, 
there  forms  on  its  surface  (immediately  over  the  orifice) 
a  hollow  depression  which  deepens  till  it  forms  a  conical 
space,  the  apex  of  which  is  at  the  orifice  towards  which 
the  liquid  flows,  while  a  rotary  movement  can  be  very 
easily  given  to,  or  transmitted  through,  its  particles. 
This  movement  must  also  augment  in  velocity  as  the 
liquid  escapes  (and  so  diminishes  the  extent  of  the 
circling  waves)  through  the  inertia  of  the  particles, 
which  tend  to  preserve  whatever  velocity  they  may  have 
gained,  and  therefore,  as  they  approach  towards  the 
centre  of  the  rotating  mass,  their  speed  must  increase 
as  the  circles  they  form  become  smaller.  If  the  orifice 
be  closed,  then  the  conical  depression  will  wander 
over  the  surface  of  the  liquid,  gradually  becoming 
shallower  and  shallower,  till  it  disappears.  The  quan- 
tities which  thus  flow  out,  in  successive,  equal  intervals, 
from  the  bottom  of  a  vessel  with  vertical  sides,  are  as 
the  diminishing  series  of  odd  numbers  9,  7,  5,  3,  i  — 
which  correspond  inversely  with  the  spaces  described  in 
equnl  intervals  by  a  falling  body.* 

The  passage  of  liquids  through  pipes  is  greatly  retarded 
by  friction  within,  and  by  the  resistance  experienced 
when  bends  take  place.  The  retardation  may  be 
diminished,  however,  by  giving  particular  forms  to  the 
commencement  and  termination  of  a  pipe  without 
otherwise  changing  its  capacity.  Thus  a  4-inch  pipe 

*  See  ante,  pp.  61  and  62. 


MECHANICS  75 

may  (whatever  its  length)  be  made  to  deliver  consider- 
ably more  water  if  its  first  three  inches  and  the  last 
yard  of  its  length,  be  enlarged  and  given  a  conical 
shape. 

The  motion  of  water  in  the  bed  of  a  river  would,  but 
for  the  resistance  offered  by  its  sides  and  its  bed,  go  on 
continually  accelerating  from  its  source  to  its  mouth, 
like  a  solid  body  falling  by  gravity.  In  that  case 
enormous  destruction  would  be  produced  in  the  lower 
lands  while  the  upper  parts  would  be  deprived  of  all 
moisture.  But  the  adherence  of  the  particles  of  water 
together,  and  the  friction  against  the  sides  and  bed 
of  the  river,  produce  a  resistance  which  increases  with 
the  velocity  of  the  current,  till  it  equals  the  accelera- 
tive  force  of  the  descent,  and  so  a  uniform  motion  becomes 
established. 

Irregularities  in  the  sides  and  beds  of  rivers  often 
produce  currents  setting  obliquely,  or  eddies,  and  of 
course  the  steeper  the  descent  of  the  river's  bed  the 
greater  the  velocity  and  force  of  the  current. 

When  a  liquid  has  any  part  of  its  surface  raised  above, 
or  depressed  beneath,  the  rest,  it  will,  as  has  been  said, 
return  to  the  general  level.  But  in  so  doing  it,  like 
a  pendulum,  acquires  a  velocity  which  carries  it  beyond 
the  position  of  equilibrium,  arid  thus  it  oscillates,  com- 
municating similar  oscillatory  motions  to  the  adjoining 
portion  of  the  surface  of  the  liquid,  and  that  to  the 
next  and  so  on.  But  as  all  these  communications  of 
motion  are  not  simultaneous  but  successive,  an  appearance 
is  produced  of  an  elevation,  or  of  a  series  of  elevations, 
travelling  along  the  surface — in  other  words,  we  have 
what  is  called  a  wave  or  a  series  of  waves. 

Each  wave  contains  particles  of  the  liquid  in  all 
degrees  of  oscillation,  elevation  and  depression,  and  the 


76  ELEMENTS   OF  SCIENCE 

breadth  of  a  wave  is  measured  between  particles  which 
are  in  similar  position,  e.g.,  from  those  at  the  greatest 
depression  in  front  of  and  behind  the  wave.  This 
dimension,  like  the  length  of  a  pendulum,  varies  as  the 
square  of  the  time  of  oscillation  and  the  velocity  of  a  wave 
varies  as  the  square  root  of  its  breadth.  Thus  if  a  boat 
be  noticed  on  one  day  to  rise  and  fall  twice  as  often  as  it 
did  on  the  previous  day,  then  the  waves  which  pass 
under  it  must  have  become  four  times  as  broad,  while 
moving  with  only  double  velocity. 

The  laws  of  hydrodynamics  have  led  to  the  construc- 
tion of  aquatic  machines  for  raising  water.  It  would 
be  quite  beyond  the  purpose  of  this  work  to  describe 
such  in  detail,  but  we  must  briefly  refer  to  the  screw 
of  Archimedes,  water-rams,  and  water-wheels. 

The  first  may  be  either  a  flexible  tube  open  at  both 
ends  and  wound  spirally  on  the  exterior  surface  of  a 
cylinder,  or  it  may  be  a  plate  of  metal  coiled  spirally 
about  an  axis  enclosed  within  a  hollow  cylinder.  The 
machine  is  fixed  in  an  inclined  position,  with  its 
lower  extremity  immersed  in  the  water  which  is  to 
be  raised. 

While  it  is  at  rest,  the  water  occupies  the  lower  part 
between  two  of  the  bends  of  the  spiral.  When  turned, 
the  machine  is  rotated  on  its  axis,  and  the  part  contain- 
ing the  liquid  being  thus  elevated,  the  water  will  be 
caused,  by  gravity,  to  descend  into  the  lower  part 
between  the  next  bends  of  the  spiral,  and  so,  in  reality, 
it  rises  with  respect  to  its  former  position  in  the  rotating 
spiral  coil  within  which  it  is  confined.  Thus  the  water 
continually  proceeds  towards  the  upper  part  of  the 
machine  from  whence  it  is  discharged. 

A  water-ram  is  a  machine  by  which  the  action  of 
gravity  on  falling  water  is  utilised  by  a  succession  of 


MECHANICS  77 

valves  which  hinder  the  moving  water  from  returning 
while  allowing  it  to  pass  freely  in  the  opposite  direction  ; 
by  this  means  it  can  be  raised  to  a  much  greater  height 
than  that  from  which  it  falls.  It  is  so  arranged 
that  a  stream  of  water  is  made,  by  its  descent,  to 
open  and  close  a  valve,  which,  each  time  it  shuts, 
drives  a  portion  of  the  water  up  another  tube  and 
to  a  higher  level,  where  it  is  again  retained  by  a 
valve,  and  so  on. 

In  water-wheels,  the  liquid  acts  as  a  moving  power  by 
its  weight,  its  momentum,  or  by  both  of  them  combined, 
acting  on  such  wheels. 

In  the  first  case,  a  wheel  is  provided  at  its  cir- 
cumference with  troughs  into  which  the  water  is 
received  near  the  level  of  the  axle  of  the  wheel ;  the 
vessels  thus  filled  becoming  heavier  than  those  on  the 
other  side,  the  wheel  is  made  to  revolve  by  mere  excess 
of  weight. 

In  the  second  case,  the  water  may  fall  into  the 
troughs  from  a  more  or  less  considerable  height  above 
the  axle,  so  as  to  add  the  increased  effect  of  the 
momentum  gained  by  it  in  its  fall.  This  is  called  an 
overshot  wheel.  An  undershot  one  has  fiat  projections 
from  its  circumference,  while  its  lower  portion  is  plunged 
in  a  stream  capable  of  turning  it. 

We  must  now  pass  to  the  last  subdivision  of  mechanics, 
namely,  that  which  relates  to  aeriform  fluids,  and  which 
is  known  as  the  science  of  pneumatics. 

Aeriform  bodies  differ  greatly  in  nature  from  solids 
and  liquids.  In  solids,  the  particles  of  which  we 
may  conveniently  suppose  them  to  consist,  are  stably 
held  together  or,  as  we  have  seen,  cohere  in  varying 
degrees  of  tenacity.  In  liquids,  the  particles  still  cohere, 
but  so  unstably  that  they  glide  over  each  other  with 


78  ELEMENTS   OF   SCIENCE 

the  greatest  ease,  and  a  liquid  presses  equally  in  all 
directions.  In  aeriform  bodies,  however,  not  only  do 
the  particles  not  cohere,  but  they  actually  repel  each 
other  and  separate  as  far  as  possible,  pressing,  however, 
equally  in  all  directions.  This  tendency  of  an  aeriform 
body  to  spread  and  diffuse  itself,  is  spoken  of  as  an 
"  extreme  elasticity,"  and  it  is  accompanied  by  an 
extreme  degree  of  compressibility.  Both  these  extremes 
are  characteristic  of  aeriform  bodies  exclusively.  Never- 
theless, like  solids  and  liquids,  they  possess  weight,  inertia, 
momentum,  and  impenetrability^not,  of  course,  that  a 
mass  of  air  is  impenetrable,  and  we  may,  with  a  finger, 
penetrate  even  into  the  mass  of  a  soft  solid  !  But  the 
real  essential  substance  of  aeriform,  as  of  all  other, 
matter,  is  deemed  to  be  impenetrable  in  the  sense  that 
it  must  always  remain  of  some  dimension  and  cannot  be 
made  actually  nothing  of. 

Aristotle  was  aware  that  air  was  a  material  substance 
and,  like  other  bodies  possessing  weight,  tended  to 
descend  towards  the  earth.  In  fact  its  weight  is  very 
considerable,  and  greatly  modifies  the  circumstances  and 
actions  of  liquids,  so  that  some  additional  facts  about 
the  latter  will  have  to  be  noted  before  concluding  this 
chapter.  Such  is  the  case  because,  in  treating  of  liquid 
bodies,  we  made  abstraction  of  the  action  of  aeriform 
ones  as  being  things  which  had  not  yet  been  brought 
before  the  reader's  cognisance. 

The  weight  of  the  atmosphere — i.e.,  of  the  aerial  mass 
round  the  surface  of  the  earth,  at  the  sea-level — is 
between  fourteen  and  fifteen  pounds  upon  every  square 
inch.  We  say  "  at  the  sea-level,"  because  it  is  obvious 
that  the  more  we  ascend  above  this  level  the  less  will  be 
the  volume  of  air  which  presses  downwards.  But  the 
decrease  in  pressure  is  very  far  from  being  uniform, 


MECHANICS  79 

because  the  lower  strata  have  to  bear  all  the  weight  of  the 
strata  of  air  above  them ;  and  the  aeriform  bodies  being 
exceedingly  compressible,  the  lower  strata  are  much  the 
denser,  and  density  rapidly  diminishes  upwards. 

The  body  of  an  ordinary  man  has  to  sustain  a  pressure 
of  about  33,600  pounds  or  15  tons  ;  but  we  are  no  more 
inconvenienced  thereby  than  is  a  fish  by  the  pressure 
of  the  ocean,  and  for  the  same  reason.*  The  property 
which  both  water  and  aeriform  substances  possess,  of 
pressing  equally  in  all  directions,  serves  no  less  to  sustain 
than  to  oppress.  Thus  the  most  delicate  glass  or  other 
vessel  is  enabled,  without  the  slightest  injury,  to  sustain 
atmospheric  pressure.  If,  however,  by  any  contrivance 
the  air  within  such  a  vessel  be  removed,  then  the  vessel 
will  be  immediately  crushed. 

There  are  machines  to  remove  air  from  a  vessel, 
as  well  as  to  force  more  into  it— such  as  an  exhaust- 
ing syringe  (for  the  former  process)  and  a  condensing 
syringe  (for  the  latter  purpose).  By  means  of  the  con- 
densing syringe,  air  may  be  added  to  what  was  already  con- 
tained, e.g.,  in  a  copper  flask  of  100  cubic  inches  capacity. 
Thereupon  the  flask  will  be  found  to  have  increased  in 
weight.  If,  on  the  contrary,  the  air  is  removed  from 
such  a  flask  by  means  of  an  exhausting  syringe,  it  will 
weigh  31  grains  less,  so  that  the  weight  of  an  ordinary 
100  cubic  inches  of  air  must  be  31  grains. 

Another  instrument  for  this  purpose  is  called  an  air- 
pump,  and  by  it  air  can  be  removed  from  the  interior  of 
a  large  and  strong  glass-vessel  called  a  "  receiver."  If 
before  it  is  emptied  (so  far  as  it  can  be  emptied)  of  air, 
a  delicate  glass-vessel,  perfectly  closed  and  containing 
air,  be  put  within  it,  then,  as  the  air  is  removed  from 

*  See  ante,  p.  70. 


8o 


ELEMENTS   OF   SCIENCE 


the  receiver  and  so  the  external  pressure,  antagonistic  to 
that  of  the  air  contained  within  the  delicate  vessel, 
ceases,  the  vessel  will  be  blown  to  pieces  by  the  unop- 
posed elastic  force  of -the  air  which  it  contained. 

Thus  it  is  plain  that  any  small  portion  of  air  so  cut 
off  from  communication  with  the  atmosphere,  still  exer- 
cises pressure  (a  pressure  that  decreases  as  the  volume 
becomes  greater),  which  cannot  be  due  to  the  weight  of 

so  small  a  portion  of  air,  but 
must  arise  from  its  expansive 
force  alone. 

As  has  been  said,  the  laws  of 
pneumatics  modify  in  various 
degrees  the  actions  of  liquids. 
Of  two  vessels,  A  and  B(Fig.i5), 
let  A  be  filled  with  water  up 
to  the  level  F,  and  B  be  empty. 
Then  let  a  bent  tube  CDE  (the 
limb  DE  being  longer  than  the 
limb  DC)  be  filled  with  water 
and  temporarily  closed  (e.g., 
with  the  finger)  at  either  end. 

Next  let  the  bent  tube  be  so  placed  that  the  end  C  be 
immersed  in  the  liquid  at  A,  while  the  other  end,  E,  is 
over  the  empty  vessel  B.  Finally,  let  both  ends  of  the 
tube  be  simultaneously  unclosed.  Then  as  gravity  brings 
down  the  water  in  the  limb  DE  it  will  be  replaced  by  a 
rise  of  water  from  A  up  the  limb  CD  to  replace  it — a 
rise  due  to  the  pressure  of  the  atmosphere  on  the  surface 
of  the  water  in  A.  By  the  continuation  of  this  process 
the  water  in  A  will  gradually  become  transferred  into 
the  vessel  B.  Such  an  instrument  is  called  a  siphon. 
The  same  action  will  result  if  the  tube  be  placed  in 
a  similar  position  empty  of  water,  provided  only  it  is 


MECHANICS  81 

also  emptied  of  air,  either  by  an  exhausting  syringe 
or  by  the  action  of  the  mouth  in  sucking.  When 
it  is  thus  emptied,  the  pressure  of  the  atmosphere  on 
the  water  in  A  immediately  causes  it  to  rise;  because 
there  is  no  longer  any  pressure  within  the  tube  to 
counteract  that  of  the  atmosphere  over  A,  the  air  in  the 
tube  having  been  removed.  Suction,  or  the  action  of 
sucking,  essentially  consists  in  the  withdrawal  of  air, 
followed  by  changes  induced  in  consequence  through 
atmospheric  pressure.  The  immersed  limb  of  the  siphon 
must  be  shorter  than  the  other,  in  order  that  the 
resultant  pressure  of  the  liquid  in  the  tube,  and  of  the 
atmospheric  pressure  may  act  in  the  direction  CDE. 
Were  both  the  limbs  of  the  tube  of  the  same  length,  the 
atmospheric  pressure  at  either  end  being  equal,  the  water 
would  then  simply  fall  back  into  the  vessels  A  and  B. 

In  a  boy's  squirt  the  principle  of  suction  is  brought 
most  simply  into  operation,  as  also  in  the  common  house- 
hold pump.  In  the  common  pump  there  is  a  valve  at 
the  bottom  of  the  space  in  which  the  piston  works,  and 
this  opens  and  allows  the  water  to  ascend  (through  the 
tube  which  dips  down  into  it)  up  to  that  space  and  so  fill 
the  partial  vacuum  produced  by  the  ascent  of  the  piston. 
Another  valve  in  the  piston  opens  to  allow  water  to 
ascend  towards  the  spout,  together  with  any  air  which 
may  be  left  to  escape,  while  the  lower  valve  simul- 
taneously closes,  and  so  prevents  the  re-descent  of  the 
water  previously  raised. 

It  was  long  supposed  that  this  ascent  of  water  was  due 
to  the  production,  by  pumping,  of  an  absolute  vacuum, 
which  being  a  thing  Nature  abhorred,  water  rose  spon- 
taneously to  fill  it.  Even  Galileo  thought  it  was  due  to 
an  attraction  exercised  on  water  by  the  piston.  A  deep 
well  at  Florence  having  failed  to  draw  water,  the 

F 


82  -    ELEMENTS   OF   SCIENCE 

attention,  first,  of  the  more  illustrious  Italian  just  named, 
and  afterwards  of  his  disciple  Toricelli,  led  to  the  discovery 
that  the  pressure  of  the  atmosphere  will  not  counter- 
balance the  weight  of  a  column  of  water  more  than 
between  33  and  34  feet  high.  Experimenting  with 
mercury,  the  last-named  observer  found  that  after 
filling  a  tube,  three  feet  long  and  closed  at  one  end,  with 
mercury,  and  immersing  its  open  end  in  a  vessel  containing 
that  fluid,  the  mercury  in  the  tube  sank  till  it  stood  about 
30  inches  higher  than  the  surface  of  the  mercury  in  the 
vessel.  The  height  of  the  mercury  sustained  by  atmo- 
spheric pressure  was  found  to  be  so  much  less  than  that 
of  water,  on  account  of  the  much  greater  density  of  the 
mercury.  The  space  left  above  the  mercury  which  had  so 
descended  was  supposed  to  be  absolutely  empty,  and  is 
known  (on  account  of  the  name  of  its  observer)  as  the 
"  Toricellian  vacuum."  This  space  is,  however,  really 
filled  with  the  vapour  of  the  liquid.  Barometers  are 
tubular  instruments  which  measure  the  weight  of  the 
atmosphere  by  showing  the  height  to  which  the  pres- 
sure of  the  air  will  raise  a  column  of  mercury  (or  other 
fluid)  contained  within  them.  As  it  is  evident  that 
the  higher  we  ascend  above  the  earth's  surface  the 
less  the  weight  of  the  atmosphere  will  be,  it  is  no 
wonder  that  barometers  serve  to  indicate  height,  when 
once  their  condition  at  the  sea-level  has  been  accurately 
ascertained.  Barometers  only  serve  to  indicate  approach- 
ing changes  of  weather  in  so  far  as  such  changes  are 
connected  with  a  denser  or  lighter  atmosphere.  That 
aeriform  bodies  may  attain  a  great  momentum  and  exer- 
cise a  vast  amount  of  pressure  is  shown  by  the  effects  of 
cyclones  and  hurricanes.  Cyclones  are  rotatory  move- 
ments of  air,  which  may  be  readily  occasioned  under 
certain  atmospheric  conditions,  on  principles  similar  to 


MECHANICS  83 

those  by  which,  as  we  have  seen,  rotatory  movements  of 
water  may  be  produced.* 

As  in  liquids,  so  in  aeriform  bodies,  movements  may 
take  place  in  the  form  of  waves.  This  is  shown  by  the 
oscillating  movements  of  the  atmosphere  near  the  surface 
of  the  earth  on  a  hot,  sunny  day  in  summer.  Such 
oscillations  are  made  manifest  by  the  apparent  twinkling 
movement  of  the  objects  seen  through  the  oscillating 
waves  of  air. 

But  these  subjects,  heat  and  the  light  which  makes 
things  visible  to  us,  are  subjects  which  pertain  not  to 
mechanics,  but  to  those  sciences,  the  elements  of  which 
will  be  briefly  introduced  to  the  reader's  notice  in  the 
next  chapter. 

Like  liquids,  aeriform  bodies  differ  much  in  density. 
This  it  is  which  makes  a  balloon  rise  in  the  air  as  bubbles 
of  oil  will  rise  in  water.  The  reason  why  a  balloon  rises 
is  that  it  contains  an  aeriform  fluid  so  much  lighter  than 
air  that  its  whole  weight  is  less  than  that  of  the  bulk  of 
air  it  displaces,  and  thus  the  relatively  heavier  air 
descends,  and  so  presses  it  upwards. 

*  See  ante,  p.  74. 


CHAPTER  IV 
PHYSICAL    FORCES 

THE  most  universal  properties — number,  figure  and 
motion — possessed  by  all  those  bodies  which  our  senses 
can  take  cognisance  of — whether  such  bodies  are  solid, 
liquid,  or  aeriform — have  now  been  treated  of  in  an 
elementary  manner. 

We  may  next  proceed  to  consider  those  forces  which 
are  commonly  said  to  affect  bodies — forces  which  bodies, 
at  any  rate,  make  manifest  to  us,  more  or  less  frequently. 
Every  one  knows  that  water  behaves  differently  at  dif- 
ferent temperatures,  and  that  the  air  is  greatly  affected 
by  heat,  as  also  that  the  same  is  true  of  solid  substances, 
though  in  very  diverse  degrees.  We  all  know  that  some 
bodies  are,  or  can  be  rendered,  luminous,  as  well  as  that 
sounds  are  transmitted  to  us  through  the  air.  Some 
readers  may  have  seen  sparks  emitted  from  the  hairs  of 
a  cat  when  rubbed,  while  others  have  doubtless,  while 
children,  amused  themselves  with  magnets,  and  no  one 
can  be  ignorant  that  the  cleanest  iron  will  get  rusty 
when  long  exposed  to  the  air. 

It  is  also  a  matter  known  to  everybody,  that  one  and 
the  same  material  substance  will  be  now  hotter,  now 
colder  ;  now  brightly  luminous,  at  another  time  dull  (as 
e.g.,  a  coal)  ;  occasionally  sonorous  and  other  times  silent 
(as  a  piano) ;  now  tranquil  and  motionless,  yet  after- 
wards conspicuously  turbulent — as  two  effervescent 


PHYSICAL  FORCES  85 

powders  will  lie  perfectly  motionless  when  mixed 
together  in  a  dry  state,  but  become  violently  turbulent, 
when  together  thrown  into  a  glass  of  water.  Every 
one  knows  that  such  changes  are  but  transitory,  as 
well  as  that  a  telegraph  wire,  however  much  used,  is 
not  perpetually  active ;  and  some  readers  (who  have 
attended  scientific  lectures)  may  probably  have  learned 
that  a  body  may  be  magnetic  or  not  magnetic,  according 
to  circumstances. 

Thus  a  conception  has  very  naturally  arisen  that 
these  manifestations  of  activity  in  material  things — 
activities  which  we  will  speak  of  as  physical  forces — 
are  entities  or  influences,  which  come  and  go — which 
pervade  bodies  for  longer  or  shorter  periods,  and  then 
leave  them — as  (to  use  a  rough-and-ready  illustration) 
a  sponge  may  be  soaked  full  of  water  and  squeezed  dry 
again,  any  number  of  times. 

The  present  chapter  will  be  devoted  to  an  exposition 
of  some  elementary  facts  concerning  these  pervading 
influences,  the  energies — or  "forces"  to  continue  the  use 
of  a  popular  term — known  as  heat,  light,  sound,  chemical 
change,  electricity,  and  magnetism. 

It  is  evident  that  bodies  which  every  now  and  then 
exhibit  any  one  of  these  forces,  continue  to  ^possess,  at 
times  when  they  do  not  exhibit  it,  the  power  of  again 
manifesting  it  when  the  necessary  conditions  return. 
The  energy  under  such  circumstances  is  said  to  be  in  a 
" potential  condition,"  as  distinguished  from  an  active,  or 
as  it  is  technically  termed,  "  kinetic,"  state.  Such  poten- 
tial energy  is  a  capacity  for  a  certain  activity — e.g.,  doing 
a  certain  amount  of  work — which  capacity  is  actively 
expended  in  overcoming  some  definite  resistance — e.g., 
overcoming  it  through  a  definite  distance — and  is  there- 
fore capable  of  measurement.  The  term  "  force  "  denotes 


86  ELEMENTS   OF   SCIENCE 

that  which  is  the  cause  of  all  and  every  known  kind  of 
motion.  As  there  are  the  six  kinds  of  active  energy 
above  mentioned,  so  we  may  speak  of  their  unknown  cause 
as  so  many  "  physical  forces  " — in  a  quite  elementary 
work,  such  as  the  present  one,  questions  as  to  the  absolute 
nature  and  distinctness  of  such  forces  cannot  be  touched 
upon,  though  conceptions  which  serve  science  as  working 
hypotheses,  will  be  referred  to. 

We  have  already  made  acquaintance  with  the  force 
spoken  of  as  gravity,  but  here  we  shall  not  further  study 
the  energy  due  to  that  force.  For  it  is  a  universal,  con- 
stant condition  of  all  material  bodies,  constant,  more- 
over, not  only  in  its  existence  and  action,  but  also  in  the 
precise  amount  of  its  action,  which  is  ever  in  exact  pro- 
portion with  the  mass  of  which  any  body  (its  distance 
from  other  bodies  being  unchanged)  consists — as  has 
been  pointed  out  in  the  last  chapter.* 

We  have  noted  the  various  modes  of  motion  and  ten- 
dencies to  motion  in  solids,  liquids,  and  aeriform  bodies, 
but  we  all  know  that  one  substance  at  least  can  exist  in 
all  three  conditions.  We  know  that  water  can  be  both 
frozen  and  changed  into  a  vapour ;  while  steam  and 
every  other  vapour  is  an  aeriform  body.  Steam  is  an 
invisible  vapour.  What  is  popularly  called  "steam"  is 
a  cloud  of  minute  particles  of  water — formed  by  the 
resumption  of  its  liquid  condition.  If  we  look  at  the 
place  where  steam  is  issuing  from  a  rapidly  boiling  kettle 
or  engine,  we  shall  find  that  nothing  is  visible  close  to 
the  mouth  of  the  spout  or  chimney,  the  cloud  of  what 
is  popularly  known  as  "  steam  "  only  begins  to  appear  at 
a  short  distance  from  it. 

HEAT. — It    is    notorious,   as   before   said,   that    cold 

*  See  ante,  p.  66. 


PHYSICAL  FORCES  87 

occasions  the  assumption  by  water  of  its  solid  form,  as 
ice,  and  that  heat  will  convert  it  into  steam.  By  the 
continued  application  of  heat,  a  vessel  of  water  may  be 
emptied — the  whole  mass  being  boiled  away  into  aqueous 
vapour,  while  when  that  vapour  passes  into  a  cooler  space 
it  becomes  condensed  into  a  cloud  of  particles  of  water — 
as  above  stated. 

A  multitude  of  other  substances  are  known  to  be 
capable  of  similar  changes  as,  for  example,  mercury.  It 
is  notorious  that  lead  can  be  easily  made  liquid  by  heat, 
and  iron  also,  though  not  as  readily.  There  is  little 
doubt  but  that  all  substances  can  exist  in  these  three 
states.  Various  gases  have  been  made  both  liquid  and 
solid,  and  Professor  Dewar  has  recently  liquefied  the 
gas  oxygen  and  even  the  air  we  breathe,  while  many 
components  or  rocks  have  been  rendered  both  liquid 
and  aeriform. 

Heat  then  is  evidently  a  very  powerful  agent  in 
effecting  the  change  of  state  from  solid  to  liquid,  and 
also  that  from  liquid  to  vapour.  Pressure  has  a  con- 
trary tendency,  but  it  requires  an  enormous  amount  of 
pressure  to  counteract  the  effect  of  a  very  little  heat. 
In  mechanics,  we  have  regarded  bodies  as  incompres- 
sible, but  in  fact  they  are  all  compressible,  though  in 
very  different  degrees.  Aeriform  bodies  are  easily  com- 
pressed, and  when  released  from  pressure,  spontaneously 
expand ;  but  extraordinary  force  is  required  to  com- 
press water,  and  greater  force  still  to  compress  solids, 
which  are  almost  incompressible. 

Liquids  may  spontaneously  pass  into  the  aeriform 
condition.  Such  is  the  case  with  water,  a  thin  layer  of 
which  will  (with  different  degrees  of  rapidity  according 
to  circumstances)  "  dry  up  "  by  a  spontaneous  process, 
called  evaporation,  by  which  it  passes  into  the  sta.te  of 


88  ELEMENTS   OF   SCIENCE 

vapour  as  in  boiling  or  "  ebullition."  Pressure  produces 
a  definite  effect  on  this  process.  Thus  the  weight  of 
the  atmosphere  causes  water  at  the  sea-level  to  need 
a  greater  supply  of  heat  to  boil  than  is  required  on 
a  very  elevated  mountain,  where  its  pressure  is 
necessarily  much  less.  By  lowering  temperature,  the 
vapour  will  again  assume  the  liquid  condition  —  as 
before  said. 

But  heat  does  not  only  act  as  a  transformer  of  bodies 
from  one  state  to  another,  it  also  exercises  one  very 
notable  effect  on  bodies  which  remain  in  an  unchanged 
condition,  whether  that  be  solid,  liquid  or  aeriform.  It 
makes  them  expand,  as  we  see  in  the  thermometer,  where- 
in heat  causes  the  liquid  it  contains  to  rise  in  a  vertical 
tube,  owing  to  the  expansion  it  produces  in  that  liquid. 
Heat  applied  to  a  gas  enclosed  in  a  vessel,  cannot,  of 
course,  expand  it  (beyond  what  may  be  allowed  by  the 
expansion  of  the  vessel  itself  from  heat)  on  account  of  its 
boundary,  but  by  its  very  gaseous  nature,  it  is  always 
expanded,  and  presses  upon  every  part  of  the  vessel 
enclosing  it,  however  low  the  temperature— supposing 
it  is  not  low  enough  to  turn  the  gas  into  a  liquid.  But 
it  will  tend  to  make  the  gas  press  more  energetically 
against  the  vessel  containing  it,  and  may  cause  that 
vessel  to  burst. 

The  whole  world  is  continually  and  everywhere  under 
the  influence  of  heat,  and  when  heat  is  passing  from  one 
body  to  another,  the  former  is  said  to  be  of  a  higher 
"  temperature "  than  the  latter,  the  temperature  of 
which  is  raised  by  the  heat  it  receives  from  the  former. 
Thus  the  terms  hot  and  cold  imply  a  relation  existing 
between  two  bodies  as  regards  their  temperature. 
There  is  absolutely  no  such  thing  as  absolute  coldness ; 
cold  is  but  a  relative  term. 


PHYSICAL   FORCES  89 

Though  bodies  expand,*  or  tend  to  expand,  through 
the  agency  of  heat,  it  is  very  evident  that  different 
bodies  and  substances  do  nob  expand  at  the  same  rate. 
Thus  it  is  plain  that  both  the  mercury  in  a  thermometer 
and  the  glass  vessel  which  holds  the  mercury  do  not 
both  expand  equally,  or  the  mercury  would  not  rise  in  it 
as  it  does. 

Liquids  expand  more  than  solids,  but  different  liquids 
as  well  as  different  solids  expand  at  different  rates. 

To  estimate  differences  of  temperature  it  is  necessary 
to  adopt  a  definite  external  standard.  This  is  necessary 
because  not  only  are  our  feelings  insufficiently  persistent 
to  enable  us  to  use  them  as  a  test,  but  (for  reasons  to  be 
explained  shortly)  they  may  positively  mislead  us  as  to 
the  relative  temperatures  of  bodies  we  successively  touch. 

The  instrument  made  use  of  is,  of  course,  the  thermo- 
meter, which  is  marked  in  a  manner  agreed  upon,  so 
that  it  may  serve  as  a  standard  of  comparison.  It  has 
been  ascertained  that  the  temperature  at  which  any 
liquid  becomes  solid  is  always  the  same,  as  also  the  tem- 
perature at  which  any  fluid  boils — the  conditions  under 
which  the  ebullition  takes  place  being  similar.  It  is 
this  fact  which  enables  a  thermometer  to  be  graduated 
— the  freezing  and  boiling  points  of  water  being  thus 
constant.  In  England  the  arrangement  adopted  is  that 
called  the  scale  of  Fahrenheit,  according  to  which  the 
space  between  the  position  of  the  mercury  in  the  tube 
when  the  thermometer  is  plunged  into  melting  ice  and 
that  at  which  it  stands  when  in  boiling  water,  is  divided 
into  1 80  spaces  or  "degrees."  The  space  below  the 
freezing  point  of  water  is  divided  into  32  similar  spaces  ; 
and  thus,  according  to  this  system,  the  freezing  point  of 

*  As  to  water,  see  post,  p.  91. 


90  ELEMENTS   OF   SCIENCE 

water  is  32°  and  its  boiling  point  32  +  180,  or  212". 
The  lowest  point  of  this  scale  is  called  "  zero,"  and  de- 
grees below  this,  are  spoken  of  as  so  many  degrees  below 
zero.  The  degrees  between  zero  and  32°  are  also  spoken 
of  as  so  many  "  degrees  of  frost."  Thus  20°  marks 
twelve  degrees  of  frost.  On  the  Continent,  Centigrade 
thermometers  are  used,  according  to  which  the  space 
between  the  points  of  freezing  and  boiling  water  is 
divided  into  100  degrees,  and  the  freezing  point  is  the 
zero  of  that  system. 

Now  if  various  bodies  of  different  kinds,  all  have  their 
temperature  simultaneously  changed  to  the  same  extent 
(all  made  10°  hotter  or  colder)  fchey  will  expand  differ- 
ently ;  that  is,  the  ratio  of  the  change  of  bulk  will  be 
different  for  every  different  substance. 

Different  substances  have,  indeed,  very  different 
capacities  for  heat,  and  the  same  amount  of  heat,  com- 
municated to  two  different  bodies  whose  masses  or  weights 
are  equal,  will  not  cause  the  same  rise  of  temperature  in 
each.  Thus  a  pound  of  water  at  40°  and  a  pound  of  mer- 
cury at  1 60°,  if  mingled  together,  will  not  produce  a  mass 
of  a  temperature  of  100°,  but  only  one  of  45°,  the  tempera- 
ture of  the  water  thus  having  only  risen  5°,  while  that 
of  the  mercury  has  fallen  115% 

If  we  take  equal  masses  of  different  bodies,  A,  B,  C, 
D,  &c.,  then  the  numbers  which  are  proportional  to  the 
various  amounts  of  heat  required  to  make  them  all  of 
the  same  temperature  are  called  the  specific  heats,  or  the 
capacities  for  heat,  of  A,  B,  C,  D,  &c.,  respectively. 

But,  as  before  said,  heat  not  only  expands  bodies,  but, 
if  continued,  will  change  solids  into  liquids  and  liquids 
into  gases.  Sometimes,  but  by  no  means  always,  solids 
will,  in  melting,  pass  through  an  intermediate,  or  jelly- 
like,  condition  before  becoming  liquid.  A  jelly  is  a  sub- 


PHYSICAL   FORCES  91 

stance  which,  for  scientific  purposes,  may  be  conceived 
of  as  being  incompressible — as  we  suppose  solids  to  be — 
while  its  particles  are  incapable  of  sliding  freely  over 
each  other,  there  being  a  partial  resistance  thereto. 

With  these  changes  of  state,  changes  of  volume  do 
not  always  correspond.  As  a  rule,  a  solid  increases  in 
volume  in  liquefying,  and  again  increases  in  assuming 
the  aeriform  condition,  while  it  shrinks  as  the  process  is 
reversed.  With  water,  however,  it  is  not  so.  In  becom- 
ing solid  (ice),  it  increases  in  bulk,  and  becomes  lighter 
than  in  the  liquid  condition. 

But  there  are  certain  notable  facts  with  regard  to 
heat  in  relation  to  such  changes  of  condition.  Heat 
curiously  disappears  during  changes  from  solidity  to 
liquidity,  and  from  liquidity  to  gaseousness,  but  re- 
appears in  changes  from,  gaseousness  to  liquidity,  and 
from  liquidity  to  solidity. 

Ice  will  absorb  a  larger  amount  of  heat  without  indi- 
cating any  rise  of  temperature,  until  the  whole  of  the 
ice  is  melted.  The  heat  so  absorbed  is  commonly  called 
heat  of  liquefaction  or  latent  heat,  as  distinguished  from 
heat  which  makes  itself  manifest.  It  is  also  called 
potential  heat,  because  it  can  reappear.  It  is  thus  again 
evolved  and  "  reappears  "  when  a  substance  passes  from 
a  liquid  to  a  solid  condition. 

If  water  be  boiled,  and  so  raised  to  a  temperature 
of  2 1 2°,  it  will  not  show  any  higher  temperature  while 
exposed  to  ordinary  atmospheric  pressure,  even  though 
an  amount  of  heat  be  applied  to  it  enough  to  raise  it 
970°.  In  this  way  much  heat  again  disappears  and 
becomes  potential,  reappearing  and  becoming  actual  and 
energetic  once  more,  when  vapour  condenses  into  the 
fluid  condition. 

Mercury  freezes  at  a  temperature  38°  below  zero,  or 


92  ELEMENTS    OF   SCIENCE 

-  38°.  Ice  (as  before  said)  melts  at  32°,  but  tin  needs  a 
temperature  of  442°  to  melt,  and  antimony  requires 
812°. 

We  have  just  seen  that  heat  can  disappear  and  become 
potential,  as  also  that  it  can  again  reappear  or  be  evolved. 
It  can  also  be — (i)  conducted,  (2)  conveyed,  (3)  radiated, 
(4)  absorbed,  (5)  reflected,  and  (6)  refracted.  The  real" 
nature  of  heat  in  itself  is  absolutely  unknown,  that  is  to 
say  it  is  only  known  through  certain  effects — itself 
remaining  permanently  inaccessible  to  our  senses. 

Various  suppositions,  or  hypotheses,  have  been 
suggested  as  to  its  nature,  the  value  of  which  depends 
on  the  extent  to  which  any  of  them  can  enable  us  to 
harmonise,  foresee,  and  predict  different  actions  of 
various  bodies,  which  are  directly  perceptible  by  us. 

It  was  at  one  time  supposed  to  be  a  peculiar  kind  of 
substance  termed  "  caloric"  But  such  substance,  it  was 
evident,  could  have  no  weight,  since  nothing  is  made 
heavier  by  being  heated,  or  having,  as  it  was  supposed, 
"  caloric  "  added  to  it.  It  could  also  exist  without  mani- 
festing itself  in  any  way — in  the  condition  just  above 
spoken  of*  as  "  latent"  or  "  potential "  heat. 

But  another  hypothesis  found  favour  subsequently; 
an  hypothesis  which,  it  will  be  seen,  is  still  more  useful 
in  reference  to  the  next  physical  energy  we  shall  consider 
—  namely,  light.  We  have  saidt  that  in  mechanics  it  is 
convenient  to  suppose  each  body  to  consist  of  a  great 
quantity  of  minute  particles,  and  the  different  supposed 
motions  of  these  supposed  particles  are  taken  to  explain 
the  diverse  conditions  we  describe  as  liquid  J  and  aeri- 
form^ Now  we  may  suppose  these  particles  to  be,  as  it 


*  See  ante,  p.  91.  t  See  ante,  p.  43. 

J  See  ante,  p.  68.  §  See  ante,  p.  78. 


PHYSICAL  FORCES  93 

were,  immersed  in  another  sort  of  fluid  substance  of  an 
indefinitely  more  refined  nature,  called  ether — a  substance 
tending  to  separate  the  particles  (and  therefore  to  oppose 
gravity),  and  also  possessed  of  and  able  to  transmit 
various  orders  of  vibratory  motions.  Motion  so  un- 
imaginably minute  taking  place  amongst  the  particles, 
or  "molecules,"  of  bodies  is  termed  molecular  motion. 
It  is  thus  distinguished  from  the  motion  of  bodies  we 
can  perceive,  which  is  called  molar  motion,  or  the  motion 
of  perceptible  masses  of  matter. 

Heat  is  now  treated  as  if  it  consisted  of  such  molecular 
oscillations,  which  are  conceived  of  as  varying  in  extent 
and  velocity,  but  as  continuing  perpetually  and  tending 
to  become  everywhere  uniform — by  intercommunication 
between  all  particles  of  all  bodies  without  limit.  Such 
intercommunication  is  supposed  to  take  place  through 
the  hypothetical  refined  substance,  called  ether,  which  is 
conceived  of  as  being  something  essentially  different  from 
the  solids,  liquids,  and  aeriform  bodies,  of  which  we  have 
hitherto  spoken,  and  also  conceived  of,  as  being  universally 
diffused.  For  some  scientific  purposes,  it  is  most  conveni- 
ent to  suppose  this  ether  to  be  an  ideally  perfect  fluid  ; 
while  for  others  it  is  treated  as  an  ideal  jelly-like  sub- 
stance.* Men  of  science  are  of  course  quite  free  to  treat 
it  in  any  fashion  which  may  help  on  investigation,  but  we 
must  not  regard  such  speculative  hypotheses  as  repre- 
senting real,  ascertained  truths.  Moreover,  as  before  said, 
an  elementary  work  like  this  is  not  the  place  to  treat  of 
such  a  problem  as  the  question  what  "heat"  in  itself  may 
be.  We  must  be  content  with  serviceable  hypotheses. 
One  such  is  that  it  consists  of  molecular  vibrations  varying 
in  intensity  and  capable  of  propagation  through  space  in 

*  See  ante,  p.  90. 


94  ELEMENTS    OF   SCIENCE 

all  direction?.  Some  facts  with  regard  to  heat  accord 
best  with  that  conception  which  regards  it  as  a  peculiar 
kind  of  fluid.  Other  facts  fit  in  best  with  the  hypothesis 
that  it  consists  of  molecular  motions ;  while  yet  other 
facts  seem  to  require  a  union  of  both  these  hypotheses. 
Such  matters,  however,  can  be  little  more  than  glanced 
at  here,  though  it  is  necessary  to  bring  some  representa- 
tion of  molecular  motion  and  of  ether,  before  the  mind 
of  any  one  who  desires  to  become  acquainted  with  the 
elements  of  science.  This  is  the  more  indispensable 
because  there  are  definite  quantitative  relations  between 
molar  motion  and  the  molecular  motion  of  heat.  The 
heat  produced  in  iron  by  the  strokes  of  the  smith's 
hammer,  and  the  occasionally  setting  on  fire  of  wheels — 
produced  by  their  revolution  (when  friction  much 
impedes  motion) — roughly  show  this  ;  but  careful  investi- 
gations have  now  revealed  precise  numerical  equivalents 
between  heat  and  the  motions  of  bodies. 

Leaving  all  hypotheses  on  one  side,  we  will  now  con- 
sider the  six  various  phenomena  of  heat  we  enumerated 
before  we  began  to  speak  of  heat  in  itself. 

(i)  Conduction. — When  two  bodies  of  different  tem- 
peratures are  placed  in  contact,  the  hotter  body  becomes 
cooler,  and  the  cooler  body  becomes  hotter,  till  both  are 
of  the  same  temperature.  When  they  are  bodies  equal 
in  mass  and  of  the  same  substance,  the  increase  of  tem- 
perature in  the  one  will  be  equal  to  the  decrease  of 
temperature  in  the  other.  Heat  is  thus  conducted  from 
one  body  to  another.  This  transference  of  heat 
takes  time,  but  the  time  varies  greatly  according  to  the 
nature  of  the  substance;  some  substances  being  much 
better  conductors  of  heat  than  others  are.  Thus  even  a. 
short  piece  of  charcoal  burning  at  one  end  can  be  held 
in  the  fingers  at  its  other  end  without  inconvenience ; 


PHYSICAL   FORCES  95 

but  a  short  piece  of  iron  made  red  hot  at  one  end  cannot 
be  so  held  :  iron  being  a  much  better  conductor  of  heat 
than  charcoal.  Wood,  woollen  substances,  and  fur,  are 
notoriously  bad  conductors  of  heat;  while  metals  are 
notoriously  good  conductors  of  it.  Gold  conducts  much 
more  than  twice  as  well  as  iron.  If  the  conducting 
power  of  gold  be  taken  as  1000,  iron  is  as  381,  while 
that  of  marble  is  but  23,  and  clay  only  n. 

We  have  before  spoken  *  of  the  insufficiency  of  our 
mere  sensations  as  measures  of  temperature.  If  the 
hand  be  plunged  in  water,  really  as  warm  as  the  air,  the 
water  will  feel  colder.  If  also  the  hand  be  placed  first  on 
fur,  then  on  a  wooden  table,  and  then  on  a  marble  one, 
the  last  will  feel  the  coldest.  This  is  because  the  marble 
is  a  better  conductor  than  the  other  substances,  and  so 
conducts  heat  more  quickly  out  of  the  warm  hand.  For 
the  same  reason  metal  will  feel  still  colder.  It  cannot 
safely  be  touched  in  the  Arctic  regions  with  the  naked 
hand,  because  it  conducts  heat  so  rapidly  from  it  as  in 
effect  to  burn  it.  If  wood  and  metal  be  both  made 
equally  hotter  than  the  hand,  the  metal  will  feel  much 
the  hotter  of  the  two,  because  it  will  conduct  heat  into 
the  hand  much  more  quickly. 

(2)  Convection. —  In  a  solid  body,  heat  passes  through 
it  without  occasioning  any  change  of  position  between 
its  constituent  parts  so  long  as  the  particles  cohere, 
but  in  liquids  it  is  quite  otherwise.  On  account  of 
their  extreme  mobility  some  of  the  particles  which 
compose  them  are  displaced  by  every  change  of  tem- 
perature— the  warmer  particles  ascending  and  so  con- 
veying the  heat  towards  other  parts  of  the  liquid 
mass,  while  by  so  doing  they  necessarily  displace 

*  See  ante,  p.  89. 


96  ELEMENTS   OF  SCIENCE 

colder  particles  which,  being  heavier,  take  the  places  of 
those  which  have  been  expanded  by  heat,  and  have  so 
become  specifically  lighter. 

In  aeriform  bodies,  convection  also  takes  place;  any 
hot  body  causing  upward  currents  at  once.  This  is  the 
cause  of  that  apparent  twinkling  movement  of  objects 
before  spoken  of  *  as  often  to  be  observed,  on  a  brilliant 
hot  day,  immediately  above  the  surface  of  the  ground. 
It  is  produced  by  waves  of  air  of  different  temperatures, 
and  therefore  of  different  densities,  which  refract  f  the 
rays  of  light,  and  so  modify  the  appearance  of  objects 
seen  through  such  waves  of  air. 

The  greater  the  power  of  convection  a  body  possesses, 
the  less  its  power  of  conduction.  Thus  water  in  a 
closed  tube  with  a  piece  of  ice  at  the  bottom  of  it 
may  be  made  to  boil  at  the  surface  while  the  ice  will 
remain  unmelted.  Aeriform  bodies  are  even  worse 
conductors  than  fluids  are. 

(3)  Radiation. — It  is  a  most  familiar  fact  that  we 
can  very  quickly  obtain  much  warmth  by  standing  in 
front  of  a  bright  open  fire  or  a  mass  of  red-hot  embers. 
This  heat  is  certainly  not  obtained  by  conduction, 
seeing  how  bad  a  conductor  of  heat  air  is.  It  is  also  not 
due  to  convection,  for  the  effect  is  too  instantaneous  and 
the  hot  air  (displaced  by  the  rush  of  cold  air  towards  the 
bright  and  glowing  mass)  would  not  be  conveyed  horizon- 
tally outwards,  but  upwards  to  the  space  whence  the 
cold  air  had  descended. 

The  fact  is  that  the  incandescent  or  glowing  mass 
gives  forth  what  are  called  rays  of  heat.  These  "  rays  " 
may  be  supposed  to  be — (a)  an  influence,  or  (b)  a  mode 
of  motion,  or  (c)  a  substance  emitted  by  the  fire  and 


See  ante,  p.  83.  t  See  post,  pp.  104  and  105. 


PHYSICAL  FORCES  97 

extending  towards  us  when  we  seek  warmth  by  standing 
near  it.  But  these  rays  are  not  only  given  forth  hori- 
zontally ;  they  are  radiated  in  all  directions — as  may  be 
proved  by  suspending  a  red-hot  sphere,  when  the  rise  in 
temperature  produced  by  it  will  be  found  to  be  equal  on 
all  sides  of  it.  The  rays  thus  given  off  proceed  in  straight 
lines. 

The  power  or  intensity  of  heat  thus  radiated  is  like 
the  force  gravity,*  in  that  it  varies  inversely  as  the 
square  of  the  distance.  It  is  four  times  less  at  two  feet 
distance  than  at  one  foot,  nine  times  less  at  three  feet, 

FIG.  16. 


sixteen  times  less  at  four  feet,  and  so  on.  This  is  because 
the  heat-rays  radiating  from  any  point  spread  out  at  a 
distance  of  two  feet  to  four  times  the  extent  of  space 
they  do  at  one  foot,  to  nine  times  at  three  feet,  sixteen 
times  at  four  feet,  and  so  on. 

All  bodies  are  constantly  radiating  away  their  heat, 
arid  as  constantly  receiving  it  from  other  bodies,  but  they 
do  this  at  unequal  rates — i.e.,  their  radiating  force  is 
unequal.  This  is  the  case  even  when  different  bodies 
are  at  the  same  temperature.  Thus  mercury  has  only 

*  See  ante,  p.  66, 


98  ELEMENTS   OF  SCIENCE 

one-fifth  of  the  radiating  power  of  lamp-black,  which  is 
almost  equalled  by  writing  paper ;  while  polished  gold, 
silver,  or  copper  has  but  little  more  than  half  that  of 
mercury.  But  the  rate  of  radiation  has  more  to  do  with 
the  state  of  the  surface  of  a  body  than  with  the  nature 
of  the  material  whereof  it  is  composed.  Bright  surfaces 
radiate  least,  but  their  power  will  be  almost  doubled  if 
their  surface  be  covered  with  lamp-black. 

Practically  the  rate  of  diminution  which  distance 
occasions  is  more  or  less  increased  by  heat  being  absorbed. 

(4)  Absorption. —  We  have  already  spoken  of  heat 
appearing  to  become  absorbed  when  it  is  rendered  latent 
or  potential ;  but  it  is  said  to  be  truly  "  absorbed  "  when 
heat  passes  from  the  radiating  to  the  conducting 
condition.  As  radiant  heat  traverses  a  body,  some  of  it 
warms  the  body  it  traverses,  and  becomes  conductable, 
but  the  amount  of  this  differs  greatly  in  different  bodies. 
None,  not  even  air,  are  what  we  may  term  absolutely 
transparent  to  heat,  or  diathermous,  but  a  certain  quantity 
of  heat  will  often  pass  completely  through  bodies.  This 
is  notably  the  case  with  the  atmosphere,  which  allows  so 
great  a  quantity  of  the  sun's  rays  to  traverse  it  without 
warming  it,  that  almost  the  entire  quantity  comes  to  the 
surface  of  the  globe,  which,  being  thus  warmed,  gives  to 
the  air,  by  convection,  that  heat  which  it  failed  to  receive 
from  the  heat  radiated  through  it.  Bodies  absorb  heat  at 
precisely  the  same  rate  as  they  radiate  it.  There  appears 
to  be  some  ground  for  supposing  that  rays  of  heat 
differ  amongst  each  other  by  some  other  quality  besides 
intensity;  since  some  rays  are  more  absorbable  than 
others,  and  so  become  filtered  out  first,  while  heat  is 
passing  through  some  more  or  less  diathermous  medium. 
The  absorbability  of  heat  differs  then  with  respect  to 
different  media,  as  we  have  just  seen. 


PHYSICAL  FORCES 


99 


A 


(5)  Reflexion. — When  considering  radiant  heat  it  is 
convenient,  since  it  always  proceeds  in  straight  lines,  to 
think  of  it  as  divided  into  an  indefinite  quantity  of 
straight  lines  or  rays  of  heat — as  we  before  found  it 
convenient  *  to  represent  the  action  of  gravity  by  a 
number  of  parallel  lines. 

As  in  dynamics  we  found  that  when  a  ball  impinges 
on  a  surface  its  angle  of  incidence  is  more  or  less 
(according  to  its  elasticity)  equalled  by  its  angle  of 
rebound,  or  of  reflexion,  so  rays  of  heat  will  rebound 
from  a  surface  according  to  the  same  law — namely,  that 
both  the  lines  of  impact  and 
rebound  must  lie  within  an 
imaginary  plane  perpendi- 
cular to  the  reflecting  sur- 
face at  the  point  of  contact. 

Thus  if  a  ray  A  (Fig.  17) 
falls  at  the  point  P,  on  a 
reflecting  surface,  it  will 
be  reflected  to  B,  and  a  line 
DP  perpendicular  to  the  sur- 
face D  will  make  the  angle 
DPB  equal  to  theangleDPA 
and  the  perpendicular,  and  both  the  incident  and  reflected 
rays,  will  all  lie  in  the  plane  CO. 

When  two  concave  reflecting  surfaces — mirrors — with 
a  certain  definite  curvature,  are  placed  opposite  each 
other,  a  very  curious  effect  may  be  produced. 

At  a  certain  distance  from  each  mirror  is  a  spot 
called  its  focus,  all  the  rays  radiating  from  which  to 
the  surface  of  the  adjacent  mirror,  will  be  reflected  in 
parallel  lines.  These  rays  impinging  on  the  surface  of 


*  See  ante,  p.  43. 


ioo  ELEMENTS    OF   SCIENCE 

the  mirror  opposite,  will  be  so  reflected  as  to  meet  again 
exactly  at  the  focus  of  the  second  mirror — the  spot  to 
which  all  the  rays  coming  to  the  mirror  in  straight  lines 
are  reflected  and  converge.  Now,  if  a  red  hot  iron  ball 
be  placed  at  A  (Fig.  18),  the  focus  of  one,  the  rays  of 
heat  will  then  radiate  from  the  adjacent  mirror's  sur- 
face, thence  they  will  be  first  reflected  in  straight  lines 
to  the  surface  of  the  other  mirror,  whence  they  will  be 
again  reflected  in  convergent  lines  to  its  focus  B — when 
if  either  a  piece  of  phosphorus  or  a  thermometer  has 
been  previously  placed  there,  the  thermometer  will 
rise  or  the  phosphorus  take  fire.  The  interposition  of 
a  screen  between  the  mirrors  will  prevent  these  effects, 

FIG.  1 8. 


while  if  there  be  no  screen,  the  red  hot  ball  may  be  placed 
even  nearer  the  thermometer  than  the  focus  of  the  first 
mirror  and  yet  produce  much  less  effect  than  when  in 
that  focus. 

(6)  Refraction.—  When  radiant  heat  passes  from  one 
medium  into  another — as  from  air  into  glass — then  the 
directions  of  its  rays  become  thereby  somewhat  changed, 
or,  as  it  is  called,  refracted.  If  the  second  medium  be 
diathermous  (transparent  to  heat)  then,  when  the  rays, 
having  traversed  it,  pass  out  of  it  again — e.g.,  from 
glass  once  more  into  air — there  is  a  second  refraction  of 
the  rays  which  completely  undoes  the  effect  of  the  first 
as  to  direction — if  (as  in  the  case  supposed)  the  third 


PHYSICAL   FORCES 


101 


medium  be  similar  to  the  first,  and  the  opposite  surfaces 
of  the  intermediate  medium  be  parallel. 

If,  however,  both  its  surfaces  be  curved  in  a  convex 
manner,  parallel  rays  falling  through  one  convex  surface 
will  converge,  and  will  converge  again  when  passing 

FIG.  19. 


out  of  the  opposite  convexity  till  they  all  meet  at  a  focus 
F  (Fig.  19). 

Thus  a  doubly  convex  lens  will  bring  the  hot  rays  of 
the  sun  to  a  focus  where  they  may  set  matter  in  com- 
bustion— the  lens  acting  as  a  "  burning  glass." 

FIG.  20. 


Doubly  concave  surfaces  (Fig.  20)  will,  in  an  analogous 
manner,  increasingly  scatter  and  disperse  the  heat  rays. 

The  refrangibility  of  heat  differs  according  to  the 
medium  it  traverses,  and  this  is  another  indication  that 
heat  rays  differ  by  some  other  quality  than  mere  intensity. 


102  ELEMENTS   OF  SCIENCE 

It  has  been  ascertained  that  some  rays  of  heat  which 
have  been  reflected,  or  refracted,  are  not  equally  energetic 
in  all  directions  to  which  they  may  (by  turning  the  reflect- 
ing or  refracting  body)  be  directed ;  but  this  phenomenon 
will  be  best  considered  when  we  treat  of  light. 

LIGHT. — There  is  great  resemblance  and  accord 
between  many  of  the  phenomena  of  light  and  those  of 
heat,  and  an  analogous  ignorance  still  exists  about  both. 
Light,  which  reveals  and  makes  known  to  us  the  world 
in  which  we  live,  remains,  like  heat,  itself  unknown. 
The  problem  as  to  its  real  nature  is,  however,  one  which 
cannot  here  be  entered  on. 

Like  heat,  again,  it  was  formerly  supposed  to  consist 
of  minute  material  particles  emitted  (by  luminous  bodies) 
in  all  directions,  but  afterwards  it  was  regarded  as  the 
effect  of  minute  vibrations,  or  waves,  of  an  elastic, 
universally  diffused  ether.  All  that  we  need  do  here  is 
to  welcome,  as  a  working  hypothesis,  that  representation 
which  best  helps  us  to  understand  and  anticipate  the 
phenomena  which  experience  presents  us  with,  keeping 
an  open  mind  about  its  truth,  and  being  ready  to  lay  it 
down  and  make  use  of  another  hypothesis  so  soon  as  any 
more  serviceable  one  may  be  forthcoming. 

The  close  connection  between  light  and  heat  is  obvious 
from  the  fact  that  we  cannot  have  light  (e.g.,  from  fire 
or  candle)  without  having  radiant  heat  also,  and  the 
warmth  to  be  felt  by  our  body  when  exposed  to  the 
brilliant  light  of  the  sun  tells  us  the  same  thing. 

It  is  abundantly  evident  that  whatever  light  may  be  in 
itself,  like  heat,  it  diffuses  itself  in  straight  lines  in  all 
directions  from  every  visible  object,  and,  of  course,  it  also 
comes  in  straight  lines  to  the  eye  from  every  visible  object. 

The  light  emitted  from  any  point  of  any  object  is  called 


PHYSICAL   FORCES  103 

a  " pencil"  and  is  said  to  consist  of  " rays "  of  light,  and 
these  can  cross  each  other  in  the  same  point  of  space 
without  either  hindrance  to  their  action  or  even  diminu- 
tion of  their  intensity.  This  may  be  shown  on  a  vertical 
white  surface  opposite  a  minute  aperture  admitting  the 
rays  of  the  sun  into  a  room  otherwise  quite  dark.  Then 
any  external  object — e.g.,  a  tree — will  be  represented 
upside  down  on  the  white  surface.  The  rays  of  light 
emanate  from  every  point  of  that  tree  in  all  directions, 
but  none  but  those  from  its  upper  part  can  reach  the 
bottom  of  the  surface  opposite  the  small  hole,  while  none 
but  those  from  the  bottom  of  the  tree  can  ascend  towards 
the  top  of  that  surface,  and  the  same  consideration 
applies  to  all  the  rays  emitted  from  each  intermediate 
point  of  the  tree's  surface.  Therefore  any  object,  thus 
viewed,  must  appear  inverted. 

Light  radiates  as  heat  does,  and  its  intensity  also 
varies  inversely  as  the  square  of  the  distance,  a  rate 
practically  diminished  by  the  absorption  it  may  undergo 
in  traversing  bodies — as,  e.g.,  the  air.  Bodies  which 
light  can  traverse  are  called  transparent.  Those  which 
entirely  absorb  it  are  opaque.  Bodies  which  are  opaque 
may  sometimes  be  rendered  transparent  very  easily.  Such 
is  the  case,  e.g.,  with  a  kind  of  agate  known  as  Hydro- 
pkane.  In  its  ordinary  condition  it  is  only  half -trans- 
parent, but  can  be  made  perfectly  so  by  immersion  in 
water.  Similarly,  paper  by  being  oiled,  can,  as  the  reader 
knows,  be  made  much  more  transparent  than  before. 

Light  travels  with  amazing  velocity — at  not  less  a 
rate  than  186,330  miles  a  second,  yet  this  does  not 
prevent  what  is  called  the  "  aberration "  of  light, 
which  will  be  explained  *  when  we  come  to  the 

*  See  post,  p.  176. 


104  ELEMENTS   OF   SCIENCE 

consideration  of  bodies  very  distant  from  the  earth's 
surface.  Light  can  travel  with  perfect  freedom  through 
any  glass  vessel,  the  interior  of  which  is  as  perfect  a 
vacuum*  as  we  can  possibly  make,  therefore  if  ether  is 
necessary  for  the  existence  of  light,  ether  must  fill  any 
such  glass  vessel,  and  therefore  its  interior  can  be  no 
real  vacuum.  Like  heat,  light  is  eminently  capable 
of  reflexion,f  wherein  it  may  be  said  to  follow  in  a 
general  way  the  laws  which  determine  the  reflexion 
of  heat.  The  quantity  of  light  reflected  varies  greatly, 
and  rarely  amounts  to  one-half — so  much  being  generally 
absorbed.  Any  object  seen  appears  the  darker,  the 
greater  the  quantity  of  light  thus  absorbed.  All  surfaces 
equally  reflect  light,  but  those  which  are  "dull"  are 
minutely  rough — i.e.,  have  minute  surfaces  turned  in 
many  different  directions  and  these  reflect  light  equally 
in  all  possible  directions.  When  a  body  appears 
"  glittering,"  it  is  because  it  bears  a  quantity  of  small 
surfaces,  or  facets,  which  are  nearly  smooth,  and  therefore 
each  such  facet  reflects  light  similarly,  and  for  the  same 
reason  a  polished  surface — as  that  of  a  mirror — appears 
to  reflect  light  most  perfectly.  It  reflects  so  perfectly, 
because  its  smoothness  causes  it  to  reflect  with  order  and 
regularity — according  to  the  law  of  equal  angles  of  inci- 
dence and  reflexion — the  rays  which  reach  it  with  order 
and  regularity  from  neighbouring  objects.  There  are 
certain  phenomena  of  reflexion  connected  with  colour 
which  will  be  best  considered  together  with  the  next 
property  of  light,  namely  refraction.^ 

Rays  of  light,  like  those  of  heat,  are  refracted  as  they 
pass  from  one  medium  into  another.     Light  falling  on  a 

*  See  also  page  60.  t  See  ante,  p.  99. 

+  See  post,  p.  108. 


PHYSICAL  FORCES 


105 


transparent  medium  is  in  part  reflected,  while  the  main 
part  which  traverses  it  becomes  refracted  on  the  way. 
It  is  this  refraction  of  the  rays  of  light  which  pass  to 
the  eye  from  all  the  parts  of  a  stick  partly  immersed  in 
water,  which  causes  the  stick  to  appear  bent  at  the 
point  where  it  enters  the  liquid,  and  also  causes  any 
solid  object  placed  on  the  bottom  of  an  empty  vessel  to 
appear  to  change  its  place  when  the  vessel  has  water 
poured  into  it. 

This  is  due  to  the  fact  that  such  rays  of  light  do  not 

FIG.  21. 


'\ 

\r 

vv 

' 

:-\ 

V 

o 

\c 

proceed  in  a  straight  line  to  the  eye  from  the  object 
looked  at,  but  are  deviated,  bent  or  refracted,  from  the 
point  where  they  impinge  upon  the  surface  of  the  second 
medium,  as  in  passing  from  the  water  to  the  air.  Thus 
it  is  that  refraction  may  enable  us  to  "  look  round  a 
corner,"  because  a  ray  of  light  proceeding  from  out 
the  water  is  bent,  by  refraction,  so  as  to  be  more  nearly 
horizontal  to  the  water's  surface. 

Let  E  (Fig.  21)  be  the  position  of  the  observer's  eye,  C 
that  of  a  coin  lying  on  the  bottom  of  a  vessel  V,  and  the 


106  ELEMENTS   OF   SCIENCE 

dotted  line  CE  be  the  direction  of  a  ray  passing  straight 
between  E  and  0.  Then  it  is  evident  that  if  an  opaque 
vertical  partition  or  septum,  such  as  0,  be  interposed 
in  the  course  of  that  straight  line,  the  coin  will  be 
invisible.  If  however  the  vessel  be  filled  with  water 
a  ray  passing  from  C  to  S,  just  above  the  summit  of 
the  septum,  will  be  refracted  to  E  for  the  following 
reasons.  A  ray  passing  from  air  into  water  always 
becomes  more  nearly  perpendicular  to  i's  surface  and 
one  passing  from  water  into  air,  always,  as  before  said, 
becomes  more  nearly  horizontal  to  its  surface,  and  so 
the  ray  CS  (from  the  coin  to  above  the  summit  of  the 
septum)  will  be  made  more  nearly  horizontal  and  thus 
pass  to  E  and  cause  the  coin  to  become  visible. 

Bays  which  fall,  or  ascend,  perpendicularly,  are  not 
refracted  at  all,  but  the  more  oblique  they  are,  the  more 
refracted  they  become,  till  they  reach  an  extreme  degree 
of  obliquity ;  when  they  are  no  longer  refracted, 
but  entirely  reflected.  This  may  be  seen  by  looking 
upwards  or  downwards  through  a  glass  vessel,  very 
obliquely,  at  the  surface  of  water  contained  within  it. 
The  water  will  then  appear  to  have  lost  all  its  trans- 
parency, and  will  reflect  as  an  ideally  perfect  mirror 
would  do.  For  the  laws  of  refraction  the  reader  must  have 
recourse,  as  for  all  that  is  not  quite  elementary  respecting 
physical  forces,  to  professed  treatises  on  physics. 

Light  passing  through  differently  shaped  transparent 
media  exemplifies  supremely  well  the  laws  previously 
stated  with  respect  to  the  passage  of  heat  through  bodies 
with  differently  shaped  surfaces.  When  light  passes 
through  glass  which  is  flat  (i.e.,  the  opposite  surfaces 
of  which  are  parallel)  it  is  of  course  doubly  refracted — 
the  refraction  undergone  on  entering  the  glass  being 
reversed  when  it  emerges  from  it  so  that  it  regains  its 


PHYSICAL   FORCES  107 

original  direction,  although  there  is  a  slight  change  of 
position.  If  the  opposite  sides  of  the  glass  are  not 
parallel  then  that  piece  of  glass  is  what  is  called  a  prism. 
By  it  the  direction  of  the  rays  is  permanently  changed, 
and  the  more  so,  the  more  inclined  to  each  other  the 
two  surfaces  of  the  glass  may  be.  It  has  also  certain 
other  effects,  respecting  colour,  which  will  be  referred 
to  a  little  further  on. 

The  light  of  day  having  so  very  distant  a  source,  may 
be  practically  regarded  as  consisting  of  parallel  rays, 
just  as  the  force  of  gravity  on  the  earth's  surface  may, 
as  we  before  saw,*  be  conveniently  treated  as  if  acting 
in  parallel  lines,  although  really  it  acts  in  lines  radiating 
from  the  earth's  centre.  Rays  of  light,  then,  which  fall 
upon  and  pass  through  bi-convex  or  bi-concave  bodies, 
follow  laws  similar  to  those  which  we  have  already  seen 
apply  to  rays  of  heat.f  Thus  it  is  that  by  a  judicious 
combination  of  glasses,  those  instruments,  so  valuable  for 
Science,  the  microscope  and  the  telescope,  are  constructed. 
Thus  also  an  image  of  external  objects  can  be  made  to  fall 
upon  the  surface  of  a  table  in  a  camera  obscura.  Bi- 
convex glasses,  or  lenses,  bring  the  rays  to  a  focus  at 
different  distances  according  to  the  curvature  of  their 
surfaces,  and  the  distance  in  each  case  is  called  ihe  focal 
length  of  such  lens. 

When  treating  of  heat,  but  very  little  could  be  said 
about  refraction.  But  now,  after  what  has  been  said 
about  light,  it  will  be  easy  to  understand  how  and  why 
rays  should  thus  be  made  to  converge  or  diverge  accord- 
ing to  the  shape  of  the  surface,  whereon  they  impinge. 
For  however  many  parallel  rays  fall  upon  a  curved 
surface,  they  must  all  have  different  inclinations  to  it, 

*  See  ante,  p.  43,  t  See  ante,  p,  101, 


io8  ELEMENTS   OF  SCIENCE 

and  must  therefore  undergo  correspondingly  different 
amounts  of  refraction.  Therefore  it  is  impossible  they 
should  be  parallel  when  they  issue  forth  from  a  body 
after  having  entered  it  through  a  curved  surface.  Every 
convex  surface  causes  convergence  of  the  rays,  and  every 
concave  surface  scatters. 

When  speaking  about  heat,  we  said*  that  there 
appeared  to  be  some  reason  for  supposing  that  its  rays 
differ  qualitatively  as  well  as  in  mere  differences  of 
intensity.  What  was  thus  suggested  as  to  heat,  is 
certain  and  evident  as  regards  light. 

No  reader  can  have  failed  to  see,  now  and  again, 
manifestations  of  colour  in  the  neighbourhood  of  some 
piece  of  glass,  or  of  crystal,  and  he  may  have  remarked 
a  resemblance  between  the  colours  thus  appearing  and 
the  hues  of  the  rainbow.  In  the  rainbow,  the  lowest  of 
the  series  of  tints  it  exhibits  is  violet,  and  to  that  succeed 
indigo,  blue,  green,  yellow,  orange,  and  red.  There  are, 
however,  so  many  intermediate  shades,  that  it  is  impossible 
to  see  where  one  ends  and  the  next  begins.  It  is  gene- 
rally believed  that  light,  which  is  apparently  colourless, 
somehow  consists  of  different  coloured  rays.  This  belief 
certainly  appears  to  be  confirmed  by  a  very  simple 
experiment.  If  a  circular  piece  of  cardboard  be  painted 
with  the  colours  of  the  rainbow,  each  patch  of  colour 
narrowing  to  a  point  at  the  centre  of  the  card  ;  then  if 
a  rod  be  passed  through  that  centre,  and  the  card  be 
turned  rapidly  round  it,  the  separate  colours  will 
disappear  and  the  card  will  assume  a  grey,  or  nearly 
white,  appearance. 

Colour  has  been  before  referred  to,t  but  its  con- 
sideration was  postponed  until  the  reflexion  of  light 

*  See  ante,  pp.  98  and  101.  t  See  ante,  p.  104. 


PHYSICAL  FORCES  109 

came  to  be  spoken  of,  because  the  hypothesis  now  popu- 
larly employed  to  explain  the  different  colours  which 
objects  present  to  us  and  seem  to  possess,  explains 
them  by  reflexion — colours  being  represented  as  due  to 
different  conditions  of  the  reflexion  of  light.  Light 
being  normally  colourless,  or  white,  a  white  object  is  one 
which  is  supposed  to  reflect  all  the  different  kinds  of 
rays  which  it  receives,  and  so  the  object  looks  white. 
Any  object  which  is  black,  is,  on  the  other  hand, 
supposed  to  absorb  all  the  rays  of  light  and  to  reflect 
none.  A  red  object  is  supposed  to  absorb  all  the  rays 
which  are  not  red,  while  the  circumstances  of  its  reflect- 
ing the  red  ones  is  supposed  to  be  the  cause  of  its  red 
appearance.  So  again  blue  and  all  other  colours  are 
supposed  to  be  similarly  caused  by  the  absorption  of 
certain  rays,  and  the  reflexion  of  those  which  seem  to 
belong  to  the  several  objects  seen  by  us  as  possessing 
corresponding  tints.  In  any  coloured  transparent  object, 
such  as  red-coloured  glass,  its  colour  is  deemed  to  be  due 
to  the  absorption  by  it  of  all  the  colours  save  the  red 
rays,  which,  being  unabsorbed,  it  transmits  to  the  eye  of 
the  spectator. 

Those  peculiar  conditions,  activities,  or  what  not,  which 
exist  in  ordinary  light  and  are  called  "  colours,"  possess 
different  degrees  of  refrangibility.  This  is  easily  shown 
by  a  simple  experiment  which  was  first  tried  by  Sir  Isaac 
Newton.  He  allowed  a  sunbeam  to  enter  a  dark  room 
through  a  small  aperture  and  throw  a  bright  spot  of  light 
on  a  screen,  placed  opposite  the  aperture  on  purpose  that 
the  beam  might  fall  upon  it.  He  then  placed  a  prism  of 
glass — the  opposite  sides  of  which  approached  each  other 
from  above  downwards  at  a  considerable  angle — in  the 
path  of  the  sun-beam.  Thereby  the  beam  became  much 
refracted,  so  that  it  produced  an  elongated  bright  spot 


no  ELEMENTS  OF  SCIENCE 

much  higher  up  the  screen  than  it  would  have  fallen  but 
for  the  prism.  When  a  broad  part  of  the  prism  was 
downwards  so  that  its  sides  approached  each  other  from 
below  upwards,  the  beam  was  reflected  downwards  instead 
of  upwards.  But  change  of  place  was  by  no  means  the 
interesting  point  of  the  experiment.  In  the  first  place 
the  bright  spot  became,  as  before  said,  elongated,  and 
secondly  it  exhibited  the  hues  of  the  rainbow — the  red 
being  lowest  and  the  violet  uppermost.  This  dis- 
persion of  the  different  coloured  rays  showed  that  they 
are  bent  (refracted)  unequally  in  passing  through  the 
prism.  The  elongated  coloured  spot  is  called  a  spectrum. 
The  ordinary  spectrum  thus  formed  by  the  sun's  light — 
called  a  solar  spectrum — may  be  said  to  be  an  elongated 
image  of  the  sun.  But  spectra  may  be  formed  by  light 
from  other  sources.  It  is  always  the  violet  rays  which 
are  the  most  refrangible,  and  the  red  which  are  the  least 
so — always  and  in  every  medium.  Nevertheless  the 
ratio,  or  proportion,  between  the  highest  and  lowest 
degrees  of  refrangibility  is  different  in  different  media, 
(e.g.,  plate  glass  thus  differs  from  flint  glass),  and  this 
enables  the  optician  to  construct  what  are  called  achro- 
matic instruments.  These  are  instruments  purposely  so 
arranged  as  to  do  away  with  the  disturbing  effects  of  the 
dispersion  of  colours  which,  without  such  aid,  would  take 
place  in  optical  instruments,  and  greatly  mar  their 
utility. 

With  the  exception  of  bodies  which  are  themselves 
luminous,  none  can  appear  of  any  colour  which  does  not 
exist  in  the  light  they  receive.  Thus  if  only  green  light 
be  supplied  to  a  red  object,  it  will  appear  neither  red  nor 
green,  but  perfectly  black ;  for  the  green  rays  will  be 
absorbed  and  not  reflected  as  such.  All  distinctions  of 
colour,  save  differences  of  intensity,  may  be  made  to 


PHYSICAL   FORCES  iir 

disappear  from  a  room  which  is  only  supplied  with  light 
of  one  amount  of  refrangibility ;  but  if  ordinary  light  be 
admitted  to  play  on  any  part  of  the  room,  the  part  so 
illuminated  will  immediately  reappear  in  its  natural 
colours.  Objects  seen  through  a  coloured  medium  or 
which  have  had  coloured  light  reflected  on  them,  appear 
— as  every  one  knows — to  be  of  the  colour  of  the  light  so 
reflected  on  them  or  of  the  colour  of  the  medium  through 
which  they  are  viewed. 

Rays  which  are  less  refrangible  than  the  red  rays 
cannot  be  recognised  by  the  eye.  If  a  body  be  raised  to 
a  temperature  of  800°  its  rays  of  radiant  heat  will  so 
illuminate  it  as  to  cause  it  to  appear  red  hot,  and  at  a 
yet  higher  temperature  such  an  object  may  appear 
white.  If  the  temperature  be  below  800°,  however,  its 
heat  rays  will  not  cause  it  to  be  visible. 

But  there  are  rays  of  light  which  are  more  refrangible 
than  those  of  violet  light.  They  cannot  act  on  the  eye  so 
as  to  produce  any  sensation  of  light,  though  they  have 
potent  effects  of  another  kind. 

It  is  these  highly  refrangible  rays  which  act  upon 
photographic  plates  and  they  can  produce  other  changes, 
on  which  account  they  are  termed  actinic,  and  sometimes 
chemical  rays.  Thus  there  are  rays  of  very  different 
degrees  of  refrangibility,  only  the  middle  series  of  which 
serve  to  illuminate  objects  and  so  can  be  recognised  by 
our  sight.  The  extremes  of  the  whole  known  series  can 
only  be  recognised  in  other  modes.  But  there  may  be 
rays  which,  as  yet,  have  not  been  recognised  in  any  way, 
and  which  may  produce  effects  of  which  we  at  present 
either  know  nothing,  or  falsely  attribute  to  other  causes. 

Nevertheless  not  all  the  rays  which  come  between 
the  actinic  and  the  heat  rays  always  make  themselves 
visible  to  the  human  eye.  This  has  been  ascertained  by 


112  ELEMENTS   OF   SCIENCE 

examining  an  exceedingly  narrow  line  of  light  passing 
through  a  very  perfect  prism.  The  spectrum  so  produced 
appears  as  a  band  of  coloured  light  which  is  continuous 
save  that  it  is  interrupted  by  very  numerous  dark  parallel 
lines  indicating  so  many  rays  which  do  not  make  their 
existence  visible.  The  arrangement  of  these  dark  lines 
is  different  in  light  derived  from  different  sources. 

As  has  been  said,  the  favourite  hypothesis  now  made 
use  of  to  co-ordinate  the  various  phenomena  of  light,  is 
that  of  regular  vibrations  or  oscillations  of  ether.  What- 
ever may  be  the  absolute  truth,  there  certainly  is  a 
definite  periodical  action  or  influence  of  some  kind  which 
takes  place  with  amazing  rapidity,  but  a  rapidity  which  is 
different  in  the  differently  coloured  rays.  For  the  sake  of 
simplicity  of  illustration,  we  may  represent  these  period- 
ical actions,  or  influences,  as  so  many  steps.  It  has  been 
ascertained  that  a  violet  ray  takes  64,631  such  steps  in 
every  inch  of  space  it  traverses.  Such  a  ray  has  been 
calculated  to  take  about  786,000,000,000,000  steps  in  a 
second,  while  a  red  ray  takes  about  449,000,000,000,000 
steps,  and  as,  when  unretarded  by  any  medium,  the  differ- 
ent rays  advance  at  the  same  speed,  the  steps  of  the  red 
ray  must  be  much  longer  than  those  of  the  violet  one. 
But  different  rays  are  retarded  unequally  in  passing 
through  different  media,  and  this  fact  explains  both  what 
is  called  the  interference  of  light  and  the  phenomena  of 
iridescence.  The  steps  taken  by  any  two  rays  of  light  of 
the  same  degree  of  refrangibility,  are  equal  in  length.  If, 
however,  they  are  together  to  produce  a  more  visible 
effect  than  a  single  ray  produces,  they  must  "  keep  step  " 
— their  actions  must  be  synchronous.  This  shows  that 
in  each  step  there  are  two  actions  or  influences,  which 
are  opposed  to  each  other  and  which  we  may  represent 
by  those  most  generalised  signs  +  and  -  . 


PHYSICAL  FORCES  113 

If  the  +  action  of  one  ray  coincides  with  the  +  of  the 
other  ray  (both  being  of  equal  intensity)  the  visible  effect 
will  be  doubled  ;  but  if  the  +  action  of  one  synchronises 
with  the  -  action  of  the  other,  the  effect  of  each  will  be 
neutralised  and  produce  darkness,  or  a  case  of  interference 
of  light.  Similarly,  if  white  light  falls  upon  any  body 
the  surface  of  which  is  minutely  varied  or  which  contains 
two  or  more  reflecting  surfaces,  the  rays,  the  steps  of 
which  are  of  different  lengths,  will  be  variously  reflected 
or  transmitted ;  and  so  the  white  light  will  break  into 
colours  and  we  shall  have  the  phenomenon  known  as 
iridescence.  Thus  it  is  that,  (i)  mother  of  pearl  (made 
up  of  extremely  thin  laminse  super-imposed),  or  (2)  a 
surface  marked  with  parallel  grooves  exceedingly  close 
together,  or  (3)  two  glass  plates  with  a  very  thin  film  of 
air  between  them,  or  (4)  the  very  thin  film  constituting 
a  soap  bubble,  will  each  and  all  appear  iridescent. 

The  last  phenomenon  of  light  to  which  we  deem  it 
here  necessary  to  refer,  is  that  termed  polarisation. 
Light  coming  from  the  sun,  or  from  any  incandescent, 
self-luminous  body,  can  be  reflected  or  refracted  equally 
well  (equally  brightly)  in  all  directions,  according  to  the 
movement  of  rotation  which  may  be  imparted  to  the 
body  which  reflects  or  refracts  it.  This,  however,  is  not 
the  case  with  light  which  does  not  come  from  a  self- 
luminous  body  but  from  one  which  merely  reflects  light. 
Such  reflected  light,  when  a  movement  of  rotation  is  im- 
parted to  the  body  which  reflects  or  refracts  it,  cannot  be 
reflected  or  refracted  equally  well  in  all  directions,  but  will 
be  more  intense  when  sent  in  some  directions  than  in 
others.  Such  light  may  be  said  to  have  acquired  "  sides," 
or  some  property  which  facilitates  its  energy  in  some  direc- 
tions and  restrains  it  in  others.  This  property  is  called 
polarity,  and  (as  we  might  now  expect  from  what  has  been 


ii4  ELEMENTS   OF   SCIENCE 

here  noted  as  to  the  resemblance  between  light  and  heat) 
analogous  phenomena  with  respect  to  heat,*  show  that 
heat  rays  have  also  their  polarity.  When  we  come  to 
consider  "  magnetism,"  we  shall  meet  with  another  kind 
of  polarity,  which  is  conspicuously  manifested  and  very 
remarkable  in  its  effects. 

SOUND.  —  As  the  recurrence  of  certain  actions,  or 
influences,  which  take  place  in  bodies,  produces  in  us 
perceptions  of  heat  or  light,  so  the  occurrence,  or 
recurrence,  of  certain  motions  of  another  kind,  produces 
in  us  perceptions  of  sound. 

If  two  solid  bodies  are  struck  together,  the  shock  of 
their  contact  gives  rise  to  a  sound,  and  certain  bodies 
are  distinguished  as  sonorous  because  very  slight 
impulses  will  cause  them  to  give  forth  very  perceptible 
sounds,  as,  for  example,  the  strings  of  a  fiddle  or  the 
metal  of  a  gong. 

An  impulse  given  to  any  body  surrounded  by  air.  is 
necessarily  imparted  by  it  to  the  immediately  adjacent 
portion  of  that  aeriform  fluid.  This,  owing  to  the 
elasticity  of  air,  rebounds  after  transmitting  an  impulse 
to  the  next  portion  of  air  and  so  on — the  impulse  being 
transmitted  by  waves  through  the  air  in  all  directions 
from  the  first  starting-point.  These  aerial  waves,  or 
oscillations,  may  be  compared  with  the  waves  which 
pass  over  the  surface  of  a  field  of  wheat  when  agitated  by 
wind,  and  they  thus  pass  along  (at  a  temperature  of  62°) 
at  a  rate  of  1125  feet  in  a  second.  The  air  of  course  does 
not  thus  pass  along  (any  more  than  the  wheat  does),  but 
only  the  waves  of  motion  traversing  it.  The  particles 
of  air,  after  each  displacement,  return  to  their  former 

*  See  ante,  p.  101. 


PHYSICAL  FORCES  115 

positions  as  the  heads  of  the  wheat  do  ;  but  the  regular 
succession  of  periodic  motions  gives  the  appearance  of 
an  onward  wave  motion  of  the  material  disturbed. 

All  sounds,  whatever  their  nature,  travel  through  the 
air  at  the  same  speed  and  pass  through  it  in  all  direc- 
tions simultaneously,  while  retaining  nevertheless  their 
distinctness — as  the  sounds  of  birds,  bells,  cattle  and 
cart-wheels  each  remain  distinct. 

Since  sound  travels  at  so  very  slow  a  rate  compared 
with  light,  it  is  easy  to  understand  how  it  is  we  do  not 
hear  the  sound  of  a  gun  till  a  very  appreciable  time 
after  we  have  seen  the  smoke  from  it.  Even  each  blow 
of  a  man  beating  carpets  some  six  hundred  or  seven 
hundred  yards  off,  will  not  be  heard  till  after  the  eye 
has  seen  the  corresponding  movement. 

Sound,  like  heat  and  light,  diminishes  in  intensity 
with  the  square  of  the  distance,  and  will  be  reflected 
according  to  the  laws  of  equal  angles.  It  is  to  this 
reflexion  that  all  echoes  are  due,  and  these  may  be 
double  or  triple  or  more  numerous,  according  to  the 
arrangement  of  the  surfaces  on  which  the  waves 
impinge. 

Waves  of  sound  which  succeed  each  other  at  equal 
intervals  and  with  sufficient  frequency,  cause  us  to  be 
aware  of  a  musical  sound  or  note.  If  the  waves  do  not 
succeed  each  other  as  quickly  as  sixteen  times  in  a 
second,  we  have  no  such  experience,  but  only  a  rattling 
sound  is  produced.  The  more  rapid  the  succession,  the 
higher  the  musical  note  perceived  ;  thirty-two  vibrations 
in  a  second  produce  almost  the  deepest  note  generally 
audible,  and  70,000  vibrations  produce  the  shrillest.  As 
we  saw  that  the  human  eye  can  only  appreciate  what 
we  take  to  be  a  certain  medium  amount  of  ether  vibra- 
tions, and  not  lower  or  more  rapid  ones,  so  the  range 


Ii6  ELEMENTS   OF   SCIENCE 

of  our  perceptions  of  musical  sounds  is  analogously 
limited.  There  are  some  persons  who  can  hear  the 
very  shrill  cry  of  the  bat,  but  to  many  it  is  quite 
inaudible. 

When  one  musical  note  is  said  to  be  an  octave  above 
another,  this  means  that,  to  reveal  it  to  us,  there  must 
be  twice  as  many  vibrations  as  in  the  case  of  the  lower 
note.  In  notes  emitted  from  the  vibrations  of  strings, 
the  longer  the  string  the  deeper  the  note,  and  to  produce 
a  note  an  octave  higher  than  that  produced  by  a  string 
of  any  given  length,  the  string  must  be  shortened  one 
half. 

There  are  what  are  called  reed  instruments  (e.g.,  the 
clarionet),  and  in  them  the  air  blown  by  the  player 
strikes  deeply  on  a  little  blade  placed  in  the  mouthpiece 
of  the  instrument  and  causes  it  to  vibrate,  so  eliciting 
various  sound?.  In  a  cornet-a-piston  there  is  no  arti- 
ficial reed,  but  the  player's  lips  are  made  to  vibrate  as 
if  they  were  two  reeds — one  on  either  side  of  the  orifice 
of  the  instrument.  The  vibrations  of  the  lips  are 
transmitted  to  the  air  within  the  cornet  which  then 
emits  very  intensified  sounds. 

Sounds  may  be  intensified  in  various  ways.  They 
will  be  so  if  sonorous  vibrations  be  transmitted  to  the 
walls  of  an  empty  box,  and  such  is  the  action  of  the 
wooden  case  of  the  violin,  without  which  the  musical 
sounds  of  the  strings  would  be  greatly  enfeebled. 

The  waves  of  air  which  occasion  musical  notes,  differ 
greatly  in  length  as  well  as  in  rapidity.  Waves  which 
occasion  very  low  notes  may  be  sixty-four  feet  long, 
whereas  high  ones  may  be  less  than  an  inch. 

Differences  of  timbre  are  due  to  the  relations  which 
may  exist  between  the  main  series  of  vibrations  and 
secondary  ones.  If  these  secondary  vibrations  are 


PHYSICAL   FORCES  117 

synchronous  with  the  primary  ones,  beauty  and  per- 
fection of  timbre  is  the  result.  When  certain  bodies 
are  in  vibration,  they  will  elicit  corresponding  move- 
ments^ called  sympathetic  vibrations — from  other  bodies. 
Thus  certain  wires  of  a  piano  may  be  made  to  vibrate 
without  being  touched  save  by  the  waves  of  air  set  in 
motion  by  another  musical  instrument  emitting  the 
notes  with  which  such  wires  of  the  piano  correspond. 
Even  the  pendulum  of  a  clock  that  has  stopped  may  be 
set  in  motion  by  the  pendulum  of  another  clock  standing 
against  the  same  wall  and  duly  oscillating. 

The  vibrations  accompanying  sound  may  be  perceived 
by  other  senses  than  the  sense  of  hearing.  Thus  the 
vibrations  of  a  tuning-fork  are  visible,  and  those  of  an 
organ-pipe  may  be  very  distinctly  perceived  by  touch, 
as  also  may  the  oscillations  of  a  deep-toned  cord. 

Air  is  a  bad  conductor  of  sound,  which  can  be  much 
better  transmitted  by  liquids  or  even  by  solids.  Water 
will  transmit  sound  more  than  four  times  as  fast  as  air, 
and  wood  or  iron  will  carry  it  seventeen  times  faster. 

ELECTRICITY.  —  The  physical  energies  yet  noticed, 
must  have  forced  themselves  on  man's  observation  from 
the  first,  but  of  those  which  remain  to  be  considered 
(apart  from  certain  isolated  phenomena)  a  knowledge 
has  been  acquired  only  during  the  last  few  centuries. 

If  sealing-wax  be  rubbed  briskly  for  some  seconds 
with  a  piece  of  cloth  or  flannel,  and  then  be  held  over 
small  fragments  of  torn  paper  within  a  distance  of  a 
quarter  of  an  inch,  such  fragments  will  immediately 
rise  and  adhere  to  it.  The  same  thing  will  occur  if  a 
glass  rod  be  similarly  rubbed  with  a  silk  handkerchief. 

If  a  small  ball,  made  of  pith,  be  freely  suspended  by  a 
silk  thread  from  some  supporting  object,  it  will  be 


ii8  ELEMENTS    OF   SCIENCE 

attracted  (like  the  pieces  of  paper)  and  adhere  either  to 
the  sealing-wax  or  the  glass  rod.  But  after  contact 
with  either,  it  will  be  repelled  and  will  diverge  in  an 
opposite  direction,  if  that  which  before  attracted  it  is 
made  to  again  approach  it.  But  though  it  will  be  thus 
repelled  by  whichever  (wax  or  glass)  was  brought  in 
contact  with  it,  it  will  be  attracted  by  the  other,  till  it 
has  come  in  contact  with  that  other,  which  will  then  in 
turn  repel  it.  Thus  the  pith  ball  may  be  first  attracted 
by  the  wax  and  then  repelled  from  it  and  attracted  by 
the  glass ;  then,  in  turn,  it  may  be  repelled  from  the 
glass  and  attracted  by  the  wax,  and  so  on  alternately 
for  any  length  of  time,  the  friction  of  the  flannel  with 
wax  and  of  the  silk  with  the  glass  being  again  and  again 
renewed.  If  two  pith  balls  be  similarly  suspended  side 
by  side,  then,  when  both  have  simultaneously  touched 
either  the  wax  or  the  glass,  they  will  not  only  be  repelled 
by  the  approach  of  whichever  of  these  they  may  have 
touched,  but  they  will  also  repel  each  other.  Neverthe- 
less this  repulsion  will  gradually  diminish,  till  they  fall 
together  side  by  side,  as  they  were  at  first,  when  it  has 
ceased  altogether. 

Thus  it  is  evident  that  some  peculiar  influence  or  energy 
is  excited  by  these  frictions,  and  the  force  producing  this 
energy  is  called  electricity.  It  is  also  sometimes  spoken 
of  as  if  it  were  itself  a  substance  of  some  kind  and  is 
often  popularly  called  the  "  electric  fluid." 

Its  real  nature  is  as  yet  entirely  unknown,  but  (like 
light  and  heat)  it  is  well  to  freely  make  use  of  any 
hypothesis  which  may  help  us  to  elucidate  and  predict 
electrical  phenomena  without  pinning  our  faith  to  the 
truth  of  any  such  hypothetical  explanation. 

There  are  also  evidently  two  kinds,  or  states,  of  elec- 
tricity :  (i)  that  produced  on  the  glass  which  is  rubbed 


PHYSICAL  FORCES  119 

by  silk  and  which  kind  is  called  positive,  or  vitreous  elec- 
tricity ;  the  other  (2),  that  produced  on  the  wax  by  the 
cloth,  is  termed  negative,  or  resinous  electricity.  Further 
each  kind  of  electricity  is  communicable  to  a  fresh  object 
by  contact  therewith. 

The  experiment  with  the  pith  balls  also  shows  that 
(a)  two  bodies  charged  with  similar  kinds  of  electricity 
repel  each  other,  and  (b)  two  bodies  charged  with  different 
kinds  of  electricity  attract  each  other. 

A  further  examination  of  such  bodies  as  we  have 
supposed  to  be  experimented  on,  will  show  us 
another  most  important  law.  If  when  the  balls  have 
been  repelled  by  the  approach  of  the  wax  after  previous 
contact  with  it,  the  flannel,  which  has  been  used  to  rub 
the  wax,  be  brought  near  them,  they  will  be  attracted 
by  it,  just  as  by  a  glass  rod  which  has  been  rubbed  with 
silk ;  while  if  the  silk  so  used  be  brought  near  them, 
they  will  be  again  repelled.  This  shows  that  at  the 
same  time  that  the  glass  is  acquiring  positive  electricity, 
the  silk  which  rubs  it  is  acquiring  negative  electricity, 
and  that  while  the  wax  is  acquiring  negative  electricity 
the  flannel  is  acquiring  positive  ;  so  that,  bearing  in  mind 
the  extended  use*  given  to  two  mathematical  signs,  the 
electricity  of  both  the  glass  and  flannel  may  be  dis- 
tinguished by  the  sign  +  and  that  of  the  silk  and  wax 
may  be  alike  denoted  by  the  sign  -  .  Hence  we  see  that 
one  kind  of  electricity  cannot  be  evoked  without  at  the 
very  same  time  evoking  the  opposite  kind  of  electricity 
somewhere  else.  So  true  is  this,  that  if  a  piece  of  glass 
have  a  small  disc  of  metal  attached  on  either  side  of  it 
and  be  suspended  by  a  silk  cord,  then,  if  one  of  these 
discs  be  made  positively  electrical,  that  alone  will  cause 

*  See  ante,  p.  25. 


120  ELEMENTS   OF   SCIENCE 

the  disc  on  the  other  side  to  become  negatively  electrical 
(and  vice  versa)  without  anything  being  directly  done  to 
the  opposite  side.  This,  as  it  were  spontaneous,  evoca- 
tion of  a  definite  and  antithetical  kind  of  electricity,  is 
called  electrical  induction. 

When  two  bodies  in  opposite  electrical  conditions  are 
brought  near  each  other  they  are  mutually  attracted, 
and  when  they  approach  within  a  certain  distance  (the 
amount  of  which  varies  with  the  intensity  of  the  elec- 
trical energy  excited)  the  electrical  energy  will  be  mani- 
fested by  a  flash  of  light  accompanied  by  some  heat  and 
a  sound.  Then  occurs  what,  on  a  small  scale,  is  called 
an  electric  spark,  and  on  a  large  scale  is  known  as  a 
flash  of  lightning.  When  this  has  taken  place  sufficiently, 
the  opposite  surfaces  will  be  found  to  be  no  longer  in 
opposite  electrical  states;  the  "  discharge,"  as  it  is  called, 
will  have  neutralised  their  opposition,  and  both  will  have 
returned  to  their  normal  and  unexcited  condition. 

But  a  phenomenon  much  more  conspicuous  and  familiar 
than  that  of  induction,  is  what  is  known  as  "  conduction." 
The  pith  balls  and  the  glass  disc  were  supposed  to  be 
suspended  by  silk,  because,  while  so  suspended,  they  can 
keep  the  electricity  they  acquire.  If  they  were  suspended 
by  a  metal  wire,  they  would  not  keep  it  at  all,  for  it 
would  instantaneously  run  away  through  such  a  channel. 
The  metal  wire  takes,  or  " conducts"  it  away  with 
extreme  rapidity  and  facility,  metals  being  extremely 
good  conductors.  Thus  bodies  may  be  arranged  in  two 
opposite  classes :  "  conductors  "  and  "  non-conductors." 
Silk,  glass,  resin,  wax,  porcelain,  and  india-rubber  are 
all  non-conductors,  and  woollen  material,  dry  wood,  and 
leather  conduct  badly.  Not  only  the  metals,  however, 
but  all  objects  containing  much  moisture,  such  as  the 
bodies  of  animals  and  plants,  are  good  conductors. 


PHYSICAL   FORCES  121 

Non-conductors  are  also  called  insulators,  because  they 
serve  to  insulate  electrified  bodies,  as  the  silk  thread 
insulates  the  pith  balls  and  so  keeps  their  electricity 
from  passing  away.  Air,  especially  dry  air,  is  a  bad 
conductor,  and  this  is  why  electricity,  when  the  tension 
becomes  too  strong,  flashes  through  it  as  a  spark,  instead 
of  being  quietly  conducted  by  it  from  one  electrified  body 
in  one  state  to  another  body  in  the  opposite  electrical 
condition.  But  air  is  not  an  absolute  non-conductor,  and 
hence  it  is  that  by  degrees  the  two  similarly  electrified 
pith  balls  slowly  part  with  their  special  electricity  and 
therewith — repulsion  ceasing — fall  together. 

Bodies  in  which  electricity  can  be  easily  excited  (e.g., 
glass  and  sealing-wax)  are  in  general  the  worst  conductors, 
but  it  seems  that  it  can  be  excited  in  all  bodies  by  friction 
and,  as  we  shall  see  later,  by  other  means  also ;  only  in 
very  many  cases  it  runs  away  by  conduction  as  quickly 
as  it  is  generated.  But  whenever  so  good  a  conductor 
as  a  metal  rod  is  fitted  with  a  glass  handle  and  so 
insulated,  it  can  be  excited  by  rubbing  and  will  retain  its 
electricity. 

The  rapidity  with  which  the  electrical  energy  travels 
is  enormous,  the  velocity  of  electrical  disturbance  (or 
energy)  being  the  same  as  that  of  light.* 

The  facts  of  conduction  and  insulation  enable  us  to 
accumulate  electrical  energy.  The  most  familiar  form 
of  its  accumulation  is  in  what  is  known  as  a  Leyden  Jar. 
This  is  a  glass  jar,  or  wide  bottle,  all  but  the  upper  part 
of -which  is  coated  both  inside  and  outside  with  tinfoil. 
The  glass  keeps  each  of  the  two  layers  of  tinfoil  insulated 
from  the  other,  and  the  inner  layer  is  entirely  insulated. 
The  neck  of  the  jar  is  then  closed  with  a  cork,  through 


*  See  ante,  p.  103. 


122  ELEMENTS   OF   SCIENCE 

which  passes  a  piece  of  metal  (wire  or  a  chain)  which 
internally  makes  contact  with  the  inner  layer  of  foil, 
while  externally  it  terminates  in  a  rounded  knob  pro- 
jecting freely  from  above  the  cork  of  the  jar. 

Then  electricity  is  produced  by  that  familiar  instrument 
called  an  electrical  machine,  which  consists  of  a  disc,  or  a 
cylinder,  of  glass,  capable  of  being  rapidly  turned  between, 
and  so  becoming  rubbed  by,  two  cushions  ;  such  action 
(as  in  the  experiment  with  the  silk  and  the  glass  rod) 
developing  electricity  on  the  glass.  This  is  collected,  as 
it  is  generated,  by  certain  metal  parts  of  the  machine, 
which  are  insulated  on  glass  legs  and  which  end  in  a 
projecting  knob,  whence  in  very  powerful  machines 
sparks  may  sometimes  be  obtained  half  a  yard  long  and 
strong  enough  to  knock  a  man  down. 

Electricity  having  been  thus  generated,  it  is  carried  by 
a  conductor  to  the  knob  on  the  Leyden  jar,  whence  it 
passes,  through  the  wire,  or  chain,  to  the  inner  coating 
of  foil  *  which  becomes  charged  with  (positive)  electricity 
when  the  outer  coating  of  the  jar  also  becomes,  by  in- 
duction, simultaneously  charged  with  electricity  of  the 
opposite  kind — in  this  case  negative.  Then  if  a  piece  of 
metal  (with  a  glass  handle  for  safety  from  shock)  be 
made  to  touch  any  part  of  the  outer  layer  of  foil  with 
one  end,  while  its  other  end  is  applied  to  the  knob  of 
the  jar,  an  instantaneous  discharge  of  electricity  takes 
place,  and  the  two  electricities  neutralise  each  other  and 
disappear.  Before  contact  is  effected,  a  brilliant  spark 
with  a  more  or  less  loud  report,  will  pass  between  the 


*  The  electricity  is  thus  by  no  means  stored  in  the  bottle,  as 
would  be  the  case  with  a  liquid.  That,  when  charged,  the 
particles  which  compose  the  glass  assume  a  peculiar  arrange- 
ment is  a  favourite  hypothesis. 


PHYSICAL   FORCES  123 

jar's  knob  to  the  conducting  piece  of  metal.  A  round 
form  is  given  to  the  knob  because  it  is  much  more  easy 
to  retain  electricity  in  a  body  of  that  shape.  In 
projecting  edges  and  points,  the  energy  becomes  so 
concentrated  and  intense,  that  it  cannot  well  be  confined 
in  bodies  so  shaped. 

When  a  metallic  circuit  is  complete,  a  current  of  elec- 
tricity may  readily  be  made  to  traverse  it,  but  the 
current  ceases  immediately  the  circuit  is  broken.  Elec- 
tricity is  conducted  along  copper  wire  with  extreme 
rapidity,  as  before  stated,  and  currents  may  be  exceed- 
ingly powerful.  If  the  metallic  circuit  through  which 
such  a  current  passes  be  of  unequal  capacity,  then  its 
thinnest  part  may  become,  and  be  maintained  at,  a  red 
or  even  a  white  heat,  reminding  us  of  the  accelerated 
flow  of  a  river  where  its  banks  approach  each  other  and 
the  stream  is  narrowed. 

Currents  of  electricity  have  very  wonderful  and  com- 
plex effects  to  which  it  is  impossible  here  to  allude  more 
than  distantly,  the  reader  being  referred,  for  all  but 
the  very  elements  of  the  science,  to  special  works  on 
Electro-dynamics  and  on  the  relations  of  electricity  to 
heat,  or  thermo-electricity. 

But  the  effects  of  currents  of  electricity  and  certain 
modes  of  their  generation,  cannot  be  understood  without 
some  elementary  notions  of  magnetism  and  chemical 
energy,  so  that  what  further  remains  for  us  to  say  about 
electricity  will  be  said  when  we  come  to  speak  of  those 
energies.*  It  may,  however,  be  here  briefly  noted 
that,  whereas  bodies  in  similar  electrical  conditions 
repel,  and  in  opposite  electrical  conditions  attract, 
each  other,  currents  flowing  in  the  same  direction 

*  See  post,  pp.  127,  133  and  134. 


124  ELEMENTS    OF   SCIENCE 

attract,  while  those  flowing  in  opposite  directions  repel 
each  other. 

Heat  and  electricity  have  very  definite  relations,  and 
a  multitude  of  more  or  less  recent  investigations  have 
enriched  the  thermal  section  of  electrical  science.  Here 
it  must  suffice  to  say  that  if  certain  metals  are  heated 
unequally,  an  electrical  current  from  the  hotter  portion  of 
the  metal  to  the  colder,  and  from  the  colder  to  the  hotter 
(if  there  is  an  uninterrupted  metallic  circuit),  will  be  set 
up.  '  A  current  may  also  be  set  up  in  a  circuit  of  conduct- 
ing material  by  the  application  of  heat  to  one  part  of  it, 
provided  the  heat  be  so  applied  that  it  does  not  diminish 
symmetrically  on  each  side  of  the  portion  most  heated. 
Thus  the  motion  of  heat  produces  electricity,  and  (as 
we  have  seen  with  respect  to  electric  currents)  the 
motion  of  electricity,  so  to  speak,  produces  heat  and 
may  produce  light. 

Some  further  effects  of  electricity  and  its  relations 
with  chemical  energy,  will  be  noticed  towards  the  close 
of  this  chapter. 

MAGNETISM. — The  common  horse-shoe  magnet,  with 
which  many  children  are  familiar,  consists  of  a  bar  of 
steel  bent  so  that  its  two  ends  come  near  each  other. 
It  has  a  slight  action  on  certain  substances,  probably 
some  action  (to  us  as  yet  imperceptible),  on  all  bodies  in 
its  vicinity,  but  a  great  and  conspicuous  effect  on  steel 
and  iron.  Needles,  iron  filings  and  other  small  iron 
bodies  are  attracted  to,  and  will  rise  and  join,  such  a 
magnet  when  its  ends  are  held  near  them.  If  a  variety 
.of  small  bodies — sand,  cinders,  small  fragments  of  wood, 
tiny  bits  of  silver  and  iron  filings — be  all  mixed  together, 
such  a  magnet  will  readily  separate  out  the  iron  particles, 
which  will  cling  in  bunches  to  its  two  ends.  Even  if  the 


PHYSICAL   FORCES  125 

iron  filings  be  spread  upon  a  piece  of  paper  or  a  thin 
sheet  of  glass,  and  the  magnet  be  moved  above  on  the 
under  surface  of  the  paper  or  glass,  the  iron  filings  will 
follow  the  magnet  so  that  its  influence  is  clearly  trans- 
mitted through  such  bodies. 

The  magnets  first  known  consisted  of  a  certain  mineral 
called  "loadstone"  which  is  especially  abundant  in 
Sweden  and  in  Asia  Minor.  Loadstones  attract  iron 
and  steel,  while  they  themselves  consist  of  an  iron  ore—- 
that is,  of  iron,  in  union  with  certain  other  substances, 
or  at  least,  resolvable  into  such. 

Artificial  steel  magnets  can  be  made  from  loadstone 
by  rubbing  them  against  that  mineral,  but  they  are  now 
also  made  in  other  ways.  A  piece  of  pure  iron,  by  contact 
with  a  natural  or  artificial  magnet,  will  itself  become 
magnetised  and  attract  iron  filings,  steel  needles,  &c.,  so 
long  as  it  remains  in  such  contact,  but  it  does  rot 
permanently  retain  its  magnetic  power.  Such  is  not  the 
case  with  steel,  which  by  contact,  or  rubbing,  will  become 
itself  permanently  magnetised. 

It  is  the  ends  of  the  magnets  which  mainly  attract, 
the  bent  part  produces  hardly  any  effect.  But  the 
actions  of  the  two  ends  are  never  alike. 

If  a  magnetised  steel  needle  be  freely  suspended  and 
allowed  to- oscillate  till  it  becomes  motionless,  then  if  one 
end,  A,  of  a  horse-shoe  magnet  be  brought  near  to  one, 
X,  of  the  two  ends  of  the  needle,  the  needle  will  be 
attracted  and  rotate  so  as  to  bring  that  end,  X,  as  close 
as  possible  to,  or  in  contact  with,  the  end,  A,  of  the 
magnet.  Then,  if  the  other  end,  B,  of  the  magnet  be 
brought  near  that  same  end,  X,  of  the  needle,  instead  of 
being  attracted,  it  will  thereby  be  repelled.  Yet  that 
same  end,  B,  of  the  magnet  will  attract  the  opposite  end 
(or  opposite  pole  Y)  of  the  needle,  which  will,  on  the 


126  ELEMENTS   OF   SCIENCE 

contrary,  be  repelled  by  the  other  pole,  or  end,  X,  which 
was  first  presented  to  the  needle. 

It  would  thus  seem,  judging  from  the  phenomena  of 
the  pith  balls  before  noted,*  that  there  are  two  kinds  of 
magnetism,  as  there  are  two  kinds  of  electricity,  and  this 
may  be  made  certain  by  the  following  simple  experiment. 
Take  two  needles,  the  ends  of  which  we  may  distinguish 
as  A  and  B.  Magnetise  them  by  rubbing  several 
times  from  the  middle  of  each  towards  the  points,  but 
towards  the  points  A  and  A  with  one  end  of  the  horse- 
shoe magnet,  and  towards  the  points  B  and  B  by  its 
other  end.  Then  evidently  the  A  poles  of  the  two 
needles  will  have  gained  one  kind  of  magnetism,  and 
their  B  poles  the  other  kind.  Thereupon  it  will  be 
found  that  both  their  A  and  B  poles  repel  each  other, 
while  the  A  pole  of  each  will  attract  the  B  pole  of  the 
other  needle  and  vice  versd.  Therefore  of  the  two  kinds 
of  magnetism — like  the  two  kinds  of  electricity — it  may 
be  said  that  like  repels  like  but  attracts  unlike. 

We  have  before  spoken  f  of  the  polarity  of  light,  but 
polarity  is  thus  especially  manifest  in  magnets  and  by 
means  of  magnetism.  The  polarity  of  magnetism  is  like 
that  of  electricity,  in  that  one  cannot  exist  without  the 
existence  of  the  other  in  its  neighbourhood.  But  two 
bodies  can  be  in  different  electrical  conditions,  each 
having  only  one  kind  of  electricity,  as  e.g.,  in  the  silk 
and  the  glass  rod.  Such,  however,  is  not  the  case  with 
magnetism,  since  every  magnetic  body  must  have,  in 
itself,  both  of  the  magnetic  polarities.  However  small 
the  fragments  into  which  a  magnet  may  be  broken, 
each  fragment  will  always  possess  both  kinds  of  mag- 
netism and  have  two  poles  and  not  one  only. 

*  See  ante,  p.  119.  f  See  ante,  p.  113. 


PHYSICAL   FORCES  127 

This  wonderful  form  of  energy,  as  before  noted,  is  not 
confined  to  iron  or  steel,  and  no  substance  is  completely 
indifferent  to  it.  Bodies  which  only  manifest  its  in- 
fluence by  being  attracted,  have  been  named  magnetics. 
Those,  the  far  larger  class,  which  are  only  repelled — 
repelled  by  both  poles — are  called  diamagnetics.  The 
wonderful  polarity  of  the  magnet  will  even  modify  the 
polarity  of  light ;  but  such  matters  are  beyond  the  range 
of  those  elementary  notions  of  science  with  which  alone 
this  work  has  to  do. 

We  have  before  spoken  of  the  relations  between 
magnetism  and  electricity,  aijd  they  are  indeed  very 
close  relations.  An  electric  current  passing  near  iron  or 
steel  tends  to  make  it  magnetic,  while  the  movements  of 
a  magnet  tend  to  produce  electric  currents.  The  rotation 
of  a  magnet  on  its  axis  will  produce  electric  currents 
through  it,  if  the  universally  necessary  condition  of  a 
current,  a  complete  circuit,  exists.  On  the  other  hand, 
the  passage  of  electric  currents  around  an  axis  will  make 
the  axis  it  surrounds  magnetic.*  Let  a  rod  of  iron  have 
an  insulated  copper  wire  wound  a  number  of  times  about 
it.  Then  so  soon  as  a  current  of  electricity  is  made  to 
pass  through  the  wire,  so  soon  will  the  rod  of  iron 
become  a  magnet — an  electro-magnet — but  its  magnetic 
energy  will  cease  the  moment  the  current  of  electricity 
is  discontinued.  The  iron  may  be  bent  as  a  horse-shoe 
and  then  if,  through  a  copper  wire  copiously  investing  it, 
a  strong  current  of  electricity  be  made  to  pass,  the  iron 
horse-shoe  will,  as  long  as  the  current  so  passes,  be  a 
very  powerful  electro-magnet,  and  sustain  a  great  weight 
of  iron,  which,  however,  will  instantly  fall  away  from  it, 
the  moment  the  current  ceases. 

*  For  a  very  important  consequence  of  this,  see  pout,  p.  171. 


128  ELEMENTS   OF  SCIENCE 

CHEMICAL  ENERGY.* — As  is  manifest  even  to  children, 
a  number  of  different  substances  exist,  such  as  sand, 
stones  of  different  sorts,  diamond?,  glass,  matter  known 
as  "  salts"  of  various  kinds,  silver,  gold,  iron,  and  other 
metals,  as  well  as  water,  quicksilver,  air,  the  gas  which 
we  burn,  &c.  &c. 

Most  of  these  bodies  can  be  "  resolved,"  by  one  or 
another  process,  into  other  substances  which  appear  to 
have  composed  them,  and  this  appearance  is  greatly 
strengthened  by  the  fact  that  the  substances  so  resolved 
can  often  be  reproduced  by  the  bringing  together,  under 
certain  conditions,  of  the  matters  into  which  they  were 
previously  resolved.  At  first  it  would  seem  as  if  such 
substances  have  been  merely  mixed,  and  that  their  com- 
ponent parts  can  be  disentangled  and  then  mixed  again. 
Such,  however,  does  not  seem  to  be  the  case. 

We  all  know  how  readily  iron  rusts  when  exposed  to 
the  air.  But  the  rust  of  iron  is  not  iron,  nor  can  we 
affirm  it  to  be  iron  mechanically  mixed  with  something  else 
so  as  to  be  able,  by  another  mechanical  process,  to  be 
separated  from  it  again.  Iron  is  one  substance,  iron  rust 
is  another  and  diverse  substance.  It  is  a  thing  of  a  differ- 
ent nature,  with  a  number  of  qualities  quite  distinct  from 
those  of  anything  which  may,  with  the  iron,  have  contri- 
buted to  form  it — to  form  the  rust.  And  another  sub- 
stance has  so  contributed — a  gas  contained  in  the  air  and 
known  as  oxygen.  This  gas,  by  acting  on  the  iron  at  its 
surface,  coalesces  with  it  to  form  the  new  substance, 
"  iron  rust,"  or  what  chemists  call  oxide  oj  iron,  and  the 
process  itself  is  called  oxidation.  By  heating  it  in  a 


*  Some  additional  information  about  chemistry  will  be  found 
in  the  next  chapter  (pp.  138  to  145),  wherein  various  properties 
of  minerals  are  considered, 


PHYSICAL  FORCES  129 

certain  manner,  the  rust  can  again  be  resolved  into 
oxygen  and  iron,  but  no  mechanical  process  will  separate 
them  from  each  other.  It  is  the  same  gas  which,  by  its 
chemical  action  on  other  substances,  causes  flame,  and  all 
our  fires  are  manifestations  of  such  chemical  energy. 

When  we  mix  together,  in  water,  the  two  finely 
divided  bodies  which  are  often  given  to  us  as  "  effervescing 
powders/'  these  two  bodies  do  not  merely  become  liquid 
and  mix.  They  each  become  resolved  into  other  sub- 
stances which  then  partly  unite  together  (in  new 
combinations  to  form  a  new  liquid  body  of  a  different 
nature)  and  partly  give  rise  to  an  aeriform  body — a  gas 
— which  escapes  from  the  liquid  in  bubbles,  so  causing 
the  effervescence.  This  is  very  different  indeed  from  a 
mechanical  mixture  such,  for  example,  as  when  we  mix 
together  two  dry  powders  of  different  colours. 

The  gas,  oxygen,  which,  by  uniting  with  iron,  forms 
"  rust,"  exists  in  the  atmosphere  mechanically  mixed  with 
the  air's  other  gaseous  components.  Water,  however, 
can  be  resolved  into  that  same  gas  and  another  gas 
called  hydrogen,  and  these  are  not  merely  mechanically 
blended.  If  these  two  gases  be  mixed,  in  due  propor- 
tion, within  a  carefully  closed  glass  vessel,  and  an  electric 
spark  be  made  to  pass  through  the  mixture,  the  two 
gases  will  entirely  disappear  and  water  will  be  found 
to  exist  in  their  stead. 

Chemical  energy  will  therefore  actually  transform  two 
or  more  substances  into  two  or  more  other  substances 
presenting  characters  which  seem  to  indicate  a  quite 
different  nature,  with  quite  different  properties.  Every 
substance  possesses  its  own  chemical  energies,  either  dor- 
mant or  potential*  (as  in  effervescing  powders  before  they 

*  See  ante,  p.  85. 


130  ELEMENTS   OF   SCIENCE 

are  mixed  in  water),  or  in  an  active,  kinetic  state  (as 
when  they  rush  together  in  their  effervescence),  and 
then  as  such  chemical  energy  ceases  and  disappears, 
it  gives  rise  to,  and  is  replaced  by,  a  definite  amount 
of  heat.  Chemical  combination  therefore  appears  to 
be  an  altogether  different  thing  from  a  mere  mixing 
or  blending  of  substances,  each  of  which  retains  its 
own  essential  characteristics.  Different  substances  may 
be  merely  mixed  in  any  proportion,  as  we  may  colour 
water  the  more  by  putting  in  it  more  indigo,  or  as 
we  may  mix  sand,  or  sulphur,  and  iron  filings  in 
any  quantity  we  like.  All  the  masses  thus  produced 
consist  of  minute  separate  particles,  each  of  which 
retains  its  own  properties.  But  if  we  mix  together 
sulphur  and  iron  filings  and  pour  some  warm  water  on 
the  mixture,  we  shall  then  have  a  manifestation  of 
chemical  energy  resulting  in  the  production  of  some- 
thing altogether  different  from  the  bodies  which  before 
existed,  more  or  less  of  which  will  be  thus  made  to 
disappear.  The  mixed  mass  becomes  hotter,  swells  and 
assumes  a  blackish  colour,  and  the  new  body  which  thus 
makes  its  appearance  is  what  chemists  call  sulphide  of 
iron.  Such  is  the  difference  between  a  mechanical 
mixture  and  a  chemical  combination. 

A  careful  study  of  the  process  of  resolving  some  sub- 
stances into  others  (called  analysis),  and  of  the  opposite 
process  of  producing  new  substances  by  the  junction  of 
others  (called  synthesis),  shows  us  that  chemical  transfor- 
mations take  place  in  an  exactly  definite  manner  as 
estimated  by  weight, 

Thus,  in  forming  sulphide  of  iron,  four  equivalent 
units  of  sulphur  and  seven  of  iron  will  disappear  and 
eleven  units  of  sulphide  of  iron  will  be  produced.  If 
there  be  more  than  this  of  either  material,  then  such 


PHYSICAL   FORCES  131 

odd  quantity  left  over  will  remain  unchanged,  alongside 
of  the  sulphide  produced. 

There  are  certain  substances  which  are  termed  "  ele- 
mentary "  and  chemical  " elements"  because  they  do  not 
seem  capable  of  being  resolved  into  other  substances, 
and  some  of  these  elements  have  an  overpowering 
attraction  for  each  other.  We  have  already  noted  that 
which  exists  between  iron  and  oxygen,  which  results  in 
the  "rust"  or  "oxide  of  iron."  Similarly,  a  metal, 
calcium,  and  oxygen  will  rush  together  and  produce  a 
rust,  or  oxide  of  calcium,  which  is  lime.  Oxygen  and 
another  metal,  termed  silicon,  will  unite  to  produce  a 
rust  known  as  oxide  of  silicon,  which  is  flint,  or  silica. 
Similarly  one  component  of  clay,  namely  alumina,  is  an 
oxide  of  yet  another  metal — aluminium. 

Not  only  elements,  but  various  compound  substances 
(so  called  because  capable  of  being  resolved  into  others), 
when  placed  in  close  proximity  to  certain  other  sub- 
stances, will  undergo  a  spontaneous  transformation  and, 
as  it  were,  exchange  partners ;  and  this  is  often  facilitated 
by  their  being  dissolved  in  water.  Thus  in  the  case  of  the 
common  effervescing  powders  before  referred  to,  we  may 
have  one  powder  consisting  of  carbonate  of  soda  (which 
can  be  resolved  into  carbonic  acid  and  soda)*  and  the 
other  powder  formed  of  the  acid  of  lemons,  or  citric  acid. 
When  these  are  simultaneously  dissolved,  the  citric  acid 
will  seize  upon  and  unite  with  the  soda,  while  the  car- 
bonic acid  of  the  carbonate  of  soda  is  set  free  and  escapes 
in  a  gaseous  form  in  the  bubbles  of  the  effervescence. 

It  may  be  that  a  substance  resolvable  into  two  ele- 
ments, may  be  robbed  of  one  of  its  elements  by  a  third 
element  placed  in  its  vicinity,  so  producing  a  new  and 

*  See  post,  p.  140. 


132  ELEMENTS   OF   SCIENCE 

different  binary  compound.  Thus  water,  as  we  have 
seen,  consists  of  two  elements,  oxygen  and  hydrogen, 
chemically  united,  and  they  are  in  the  proportion  of  two 
volumes  of  hydrogen  for  one  volume  of  oxygen.  Now  a 
very  light  metal,  known  as  potassium,  and  oxygen,  have 
an  extreme  chemical  affinity  for  each  other.  This  is  so 
great  that  if  a  piece  of  potassium  be  thrown  into  water 
the  chemical  energy  thus  developed  is  of  such  intensity 
that  heat  and  light  are  produced  in  the  water,  by  the 
energetic  junction  of  some  of  the  oxygen  of  the  water 
with  the  metal,  which  burns  (so  forming  potash  or  oxide 
of  potassium),  while  such  of  the  hydrogen  of  the  water 
as  is  thus  abandoned  by  its  oxygen,  being  set  free, 
also  burns  in  uniting  energetically  with  the  oxygen  in 
the  air,  so  forming  aqueous  vapour.  Another  such 
reciprocal  interchange  of  elements  will  take  place  if 
we  put  together  the  two  substances  respectively  known 
as  "  nitrate  of  silver  "  and  "  hydrochloric  acid."  Nitrate 
of  silver  is  resolvable  into  silver,  nitrogen  and  oxygen, 
there  being,  by  weight,  three  times  as  much  oxygen  as 
either  of  the  others.  The  hydrochloric  acid  consists  of 
the  gases  chlorine  and  hydrogen.  When  these  two  sub- 
stances are  placed  in  proximity,  the  chlorine  will  leave 
the  acid  to  unite  with  the  silver  of  the  nitrate  of  silver, 
and  so  produce  what  is  called  chloride  of  silver,  while 
the  hydrogen  of  the  acid  unites  with  the  nitrogen  and 
oxygen  of  the  nitrate  of  silver  and  so  forms  nitric*  acid. 
It  is  practically  most  useful,  in  the  study  of  chemistry, 
to  regard  each  substance  as  made  up  of  minute  particles 
called  " molecules"  and  these  again  of  still  more  minute 
particles  termed  "atoms"  combined  in  definite  proportions 

*  As  to  "nitrates,"  "carbonates,"  "sulphates,"  "phosphates," 
and  for  other  examples  of  chemical  change,  see^o«s£;  pp.  139-142. 


PHYSICAL   FORCES  133 

— as  estimated  by  weight — according  to  what  is  known  as 
the  "  atomic  theory"  A  whole  series  of  symbols  has  been 
devised  to  conveniently  denote  such  conditions ;  thus  water 
is  imagined  to  be  made  up  of  molecules,  each  of  which  is 
composed  of  two  atoms  of  hydrogen  and  one  atom  of  oxy- 
gen. Water  therefore  is  represented  by  the  symbol  H2O, 
and  H2SO4  stands  for  sulphuric  acid — S  signifying  sulphur. 
Similarly,  a  multitude  of  analogous  symbols  serve  to 
denote  a  multitude  of  different  substances.  This  system 
is  of  enormous  practical  utility,  and  demands  the  most 
careful  study,  though  the  absolute  constitution  of  matter 
remains  unknown  to  us.  For  farther  information  about 
the  laws  concerning  the  proportions  in  which  different 
elements  and  chemical  substances  combine,  and  the  sym- 
bols made  use  of  to  denote  such  proportions,  the  reader 
must  have  recourse  to  treatises  on  chemistry. 

Chemical  energy  is  very  closely  related  to  the  other 
physical  energies.  It  not  only  occasions  warmth  but 
may  be  greatly  facilitated  thereby,  while  the  heat  and 
light  it  may  occasion  can  be  made  manifest  by  acting 
as  just  described,  with  potassium.  It  is,  however,  also 
exemplified  by  every  fire  and  every  candle  which  we  see 
burning,  since  every  such  phenomenon  is  both  a  result 
and  a  sign  of  the  exertion  of  chemical  energy.  Chemical 
energy  is  most  intimately  related  to  electricity.  Indeed 
the  resolution,  by  chemical  energy,  of  different  sub- 
stances is  always  accompanied  by  some  electrical  change. 

An  electric  current,  on  the  other  hand,  can  produce 
chemical  changes  in  substances  through  which  it  passes, 
and  so  bring  about  changes  not  as  yet  otherwise  pro- 
ducible, as  we  have  just  seen  with  regard  to  a  spark 
traversing  a  mixture  of  oxygen  and  hydrogen  and  so 
evolving  water.  There  are  certain  chemical  substances 
termed  acids  (e.g.,  sulphuric  and  nitric  acid),  and  others 


134  ELEMENTS   OF   SCIENCE 

termed  alkaline  substances,  each  of  which  latter  is  also 
called  a  base.  Bodies  composed  of  an  acid  and  a  base 
are  termed  "  salts."  Now  if  the  two  poles  (the  ends  of 
the  wires)  of  an  electric  pile  or  battery  be  placed  in 
water  so  that  the  electricity  may  be  conducted  through 
it  from  one  pole  to  the  other,  and  any  "  salts  "  be  dis- 
solved in  that  water,  we  shall  find  the  solution  breaks  up, 
the  acid  matter  going  to  the  positive  pole,  and  the  base, 
or  alkaline  constituent,  to  the  negative  pole.  This 
strikingly  demonstrates  the  close  connection  which 
exists  between  electrical  and  chemical  energy.  The 
quantity  of  electricity  generated  by  chemical  changes 
is  often  enormous.  It  has  been  said  that  the  resolution 
of  a  grain  of  water  will  generate  a  quantity  equal 
to  a  flash  of  lightning.  As  in  the  generation  of 
heat,  light  and  magnetism  by  chemical  energy,  so  also 
in  its  generation  of  electricity,  the  quantity  generated 
bears  a  constant  and  exact  relation  to  the  amount  of 
chemical  energy  expended. 

The  mode  in  which  electricity  is  most  commonly  and 
effectively  generated  by  chemical  energy  and  a  powerful 
electric  current  induced,  is  by  what  are  called  electric 
batteries  and  piles.  The  simplest  and  most  primitive 
form  of  the  electric  pile  consists  of  a  series  of  discs  of 
zinc  and  copper,  separated  by  discs  of  cloth  soaked  with 
vinegar,  and  with  two  wires  fastened  to  the  series.  One 
of  these  wires  must  touch  a  disc  of  copper  at  one  end  of 
the  pile  and  the  other  must  be  in  contact  with  a  disc  of 
zinc  at  the  other  end  of  the  pile,  while  each  wire  projects 
freely  at  its  other  end.  The  chemical  energy  excited 
by  the  contact  of  the  substances  in  the  pile  gives  rise 
to  electricity,  and  therefore  to  both  its  so-called  kinds. 
The  positive  kind  goes  exclusively  to  the  wire  which 
touches  the  copper,  while  that  from  the  zinc  receives 


PHYSICAL   FORCES  135 

the  negative  electricity.  If  now  the  two  free  ends 
of  the  wires  be  joined,  a  current  will  be  immediately 
established,  and,  by  making  such  a  current  pass  round 
iron,  magnetism  is,  as  before  stated,  necessarily  and  at 
once  induced. 

By  means  of  small  porcelain  jars,  conjoined  in  various 
series,  and  each  supplied  with  an  acid  fluid  in  which 
portions  of  copper  and  zinc  are  suspended,  powerful 
generators  of  electricity  (batteries)  are  formed,  the  wires 
from  either  extremity  of  which  (bearing,  to  speak  popu- 
larly, different  electricities)  will,  by  their  approximation, 
chemically  resolve  many  substances  and  will  emit  small 
sparks  at  each  contact.  When  these  currents  are  made 
to  pass  between  small  pieces,  or  delicate  filaments,  of 
pure  charcoal  attached  one  to  the  end  of  each  wire, 
the  brilliance  we  know  as  "  the  electric  light "  will  be 
generated.  Such  currents  also  serve  to  work  the  elec- 
tric telegraph,  the  telephone,  and  the  microphone,  which 
here  we  can  do  no  more  than  name. 

Chemical  changes  between  certain  bodies  may  be 
induced  by  the  mere  proximity  of  similar  changes  going 
on  in  other  bodies,  and  examples  of  this  process  are  met 
with  in  photography. 

When  chemical  energy  takes  place  with  great 
intensity,  it  is  generally  accompanied  by  light  and  heat 
and  the  quantitative  relations  before  referred  to*  as 
existing  between  them,  and  between  them  and  magnet- 
ism and  electricity,  reveal  to  us  a  profound  similarity 
between  all  known  physical  energies. 

As  to  what  chemical  energy  is  in  itself,  we  know  no 
more  than  we  do  with  respect  to  the  other  forms  of 
energy.  It  may  be  that  there  is  in  Nature  either  one 

*  See  ante,  p.  102. 


136  ELEMENTS   OF   SCIENCE 

unimaginable  form  of  energy  which  manifests  itself 
according  to  circumstances — as  heat,  light,  electricity, 
magnetism  and  chemical  energy ;  or  else  that  there  are 
fundamentally  different  forms  of  force  which  have  be- 
tween them  relations  of  quantitative  equivalence  as  they 
act.  The  former  is  the  view  now  popular.  These,  how- 
ever, are  questions  so  remote  from  the  mere  elements 
of  science,  that  we  will  no  further  deal  with  them  here, 
but  proceed  to  consider  that  real  world  wherein  all  these 
physical  energies  play  their  several  parts. 


CHAPTER  V 
THE  NON-LIVING  WORLD 

HAVING  now  made  some  acquaintance  with  the  laws 
which  regulate  the  stability  and  movements  of  bodies, 
and  with  the  various  forces  which  may  energise  in  them, 
we  may  next  proceed  to  survey  the  actual  world  about 
us.  We  have  to  study  the  nature,  structure  and 
properties  of  the  parts  which  actually  compose  it,  and 
the  various  ways  in  which,  as  a  whole,  it  is  modified  by 
the  physical  forces  which  act  upon  it,  making  abstrac- 
tion, however,  of  the  phenomena  of  life.  We  assume 
that  the  student  knows  the  earth  to  be  globular,  with  a 
north  and  south  pole  equidistant  from  the  equator ;  also 
that  its  surface  is  described  by  means  of  imaginary 
circles,  parallel  with  the  equator,  marking  degrees  of 
latitude,  and  by  others  which,  at  right  angles  with  the 
former,  pass  through  the  poles  and  serve  to  indicate 
degrees  of  longitude.  The  world  is  everywhere  sur- 
rounded by  an  aeriform  mass,  the  atmosphere,  while  the 
greater  part  of  its  surface  is  covered,  more  or  less  deeply, 
by  water.  Its  solid  mass  is,  as  every  one  knows,  composed 
of  a  variety  of  matters,  such  as  different  kinds  of  earth, 
some  being  clay,  some  sand,  &c.,  with  many  stones 
scattered  through  and  over  its  soil,  while  large  tracts 
are  composed  of  rocks.  These  rocks  may  be  sandstones, 
slate,  granite,  limestone  or  chalk,  &c.,  and  the  rocks 
may  contain  metals,  metallic  ores  or  crystals.  The 


138  ELEMENTS   OF   SCIENCE 

whole  mass  of  different  substances  which  thus  make  up 
the  solid  substance  of  the  globe  are  termed  "  minerals." 

As  was  pointed  out  in  the  last  chapter,  most  of 
these  bodies  can  be  resolved  into  other  substances,  and 
ultimately  into  "  elements" — so  called  because  they  have 
not  been  found  capable  of  further  chemical  analysis. 
There  are  about  seventy  substances  which  are  thus  pro- 
visionally regarded  as  ultimate,  and  which,  by  most  varied 
and  different  degrees  of  chemical  synthesis,  compose  all 
those  matters  whereof  the  world  consists.  But  however 
varied  may  be  the  degrees  of  synthesis  produced,  the  ele- 
ments, as  before  said,*  are  always  combined  in  each  kind 
of  substance,  in  one  exactly  definite  manner,  as  estimated 
by  weight.  Of  the  various  elements,  some,  at  what  to  us 
are  normal,  moderate  temperatures,  are  aeriform.  Such 
are  the  gases  before  spoken  of  as  oxygen  or  hydrogen,"3?  and 
also  the  gases  nitrogen  and  chlorine,  with  various  others. 
All  the  metals  are  elements  and  are  normally  solid,  though 
mercury,  as  we  know,  is  liquid.  Amongst  the  metals 
are  calcium,  silicon,  aluminium,  potassium,  sodium,  mag- 
nesium, and  arsenic.  Other  solid  elements  are  carbon 
(or  pure  charcoal),  sulphur,  phosphorus,  and  iodine. 

Oxygen  at  all  ordinary  temperatures  is  a  colourless 
gas,  but  it  has  lately  been  changed,  by  reducing  it  to  an 
extremely  low  temperature,  to  the  condition  of  a  blue 
liquid.  As  we  have  seen,  it  has  a  great  tendency  to  unite 
itself  with  many  other  substances.  When  it  unites 
violently,  the  substance  it  unites  with  "  burns."  A 
general  process  of  union,  such  as  the  rusting  of  iron,  may 
be  therefore  called  a  slow  combustion.  Anything  which 
burns  in  the  air,  burns  with  far  greater  intensity  and 
brilliancy  when  plunged  in  oxygen.  Nevertheless,  though 

*  See  ante,  p.  133.  f  See  ante,  p.  129. 


THE   NON-LIVING   WORLD  139 

the  greatest  agent  in,  and  supporter  of,  combustion, 
oxygen  itself  is  incombustible  in  air.  Various  of  its 
combinations  or  "  oxides  "  have  been  already  noted.* 

Hydrogen  does  burn  in  air,  though  it  cannot  aid  com- 
bustion. It  is  the  lightest  substance  known,  and  forms  the 
chemical  standard  or  unit  of  weight,  and  is  very  widely 
diffused.  Water  can  be  resolved  f  into  twice  as  much 
hydrogen  (estimated  by  volume)  as  oxygen,  and — as  was 
stated  in  the  last  chapter — into  one  part  of  hydrogen  to 
eight  of  oxygen  as  estimated  by  weight.  Water  may 
be  called  an  oxide  of  hydrogen,  and  hydrogen  may  be 
regarded  as  an  aeriform  metal. 

Nitrogen  differs  greatly  from  oxygen,  save  that, 
like  oxygen,  it  is  colourless.  It  is  extremely  indisposed 
to  unite  with  other  elements,  and,  so  far  from  promoting 
combustion,  it  stops  it,  extinguishing  a  flame  plunged 
into  it.  It  is  remarkable  also  for  the  extreme  instability 
of  the  compounds  of  which  it  forms  a  part,  such  as 
gunpowder,  gun-cotton,  nitre-glycerine,  and  iodide,  sul- 
phide and  chloride  of  nitrogen.  These  constitute  a 
series  of  substances  successively  exploding  with  greater 
and  greater  violence  and  readiness.  Nitrogen,  neverthe- 
less, is  itself  incombustible  in  air.  In  conjunction  with 
oxygen  it  forms  nitric  acid,  which,  when  united  with 
other  substances,  produces  what  are  called  "  nitrates" 

One  notable  substance  that  is  resolvable  into  nitrogen 
and  hydrogen,  is  ammonia,  which,  under  ordinary  circum- 
stances, is  a  gaseous  as  well  as  alkaline  \  substance.  It 
is  colourless  but  very  pungent,  and  dissolves  in  water 
with  extreme  rapidity,  that  liquid  at  50°  Fahr.  con- 
densing 670  times  its  own  volume  of  ammonia. 

*  See  ante,  p.  131.  f  See  ante,  p.  132. 

J  See  ante,  p.  134. 


140  ELEMENTS    OF   SCIENCE 

Chlorine  is  a  gas  of  a  green  colour,  and  can  be  com- 
pressed into  a  yellow,  limpid  liquid  when  subjected  to  a 
pressure  about  four  times  that  of  the  atmosphere,  but 
rapidly  becomes  again  gaseous  when  such  pressure  is 
removed.  Like  oxygen,  it  is  a  supporter  of  combustion, 
and  powdered-antimony  when  thrown  into  it  burns  spon- 
taneously. It  possesses  a  powerful  and  peculiar  odour. 
Many  of  its  compounds  are  termed  chlorides,  and,  united 
with  the  metal  sodium,  it  forms  chloride  of  sodium,  or 
"  common  salt." 

Carbon  is  an  element  which  remains  solid  even  at  the 
highest  temperatures  yet  applied  to  it,  but  it  is  rarely 
found  pure.  As  such  it  may  exist  in  one  of  three  different 
conditions — (i)  as  pure  charcoal;  (2)  as  black-lead  or 
graphite ;  and  (3)  as  the  diamond.  It  is  very  abundant 
united  with  oxygen.  Such  oxide  of  carbon,  or  carbon 
"rust,"  is  a  gas  at  all  ordinary  temperatures  and 
pressures,  though  by  extreme  pressure  it  has  been  made 
liquid  and  also  solid.  It  is  commonly  known  as  "  carbonic 
acid,"  and  since  it  is  formed  by  the  union  of  charcoal 
with  oxygen  (six  parts,  by  weight,  of  carbon  to  sixteen 
parts  of  oxygen),  it  is  given  off  abundantly  where  coal  fires 
are  burned.  It  is  a  colourless  gas  with  little,  if  any, 
odour,  and  a  burning  candle  plunged  into  it  becomes  extin- 
guished. United  with  a  variety  of  other  substances  it 
produces  what  are  known  as  carbonates,  such  as  carbonate 
of  lime  and  carbonate  of  soda.  Four  equivalents  of  car- 
bon, four  of  oxygen,  and  two  of  hydrogen,  constitute 
citric  acid,  so  commonly  used  for  effervescing  drinks. 
This  acid  will  unite  with  other  substances,  such  as 
ammonia,  potash,  soda,  and  lime,  forming  a  citrate  of 
each  respectively. 

Sulphur. — This  yellow  elementary  mineral,  commonly 
called  "  brimstone"  is  normally  a  solid ;  but  a  small 


THE   NON-LIVING  WORLD  141 

heat  will  render  it  liquid,  and  a  little  more  will  make 
it  aeriform.  Then,  if  a  cold  surface  be  brought  near, 
it  will  again  become  solid,  being  deposited  on  that 
surface  in  the  form  of  minute  grains,  known  as  "  flour 
of  sulphur."  But  besides  its  liquid  and  gaseous  states, 
sulphur  may  exist  in  more  than  one  solid  condition,  and 
may  be  made  to  pass  alternately  backwards  and  for- 
wards, from  one  solid  condition  to  the  other,  by  means 
of  slight  changes  of  temperature.  One  of  these  is  known 
as  crystalline  sulphur,  while  the  other  is  non-crystalline.* 
Substances  which'crystaUise  in  two  different  forms,  with- 
out change  of  nature,  are  called  dimorphic;  and  those 
which,  like  carbon,  can  exist  in  more  than  two,  are  termed 
polymorphic.  The  same  body  may  possess  distinct  pro- 
perties, and  any  one  such  state  contrasted  with  another, 
is  said  to  be  an  "  allotropic  "  state.  Thus,  we  say  crystal- 
line sulphur  can  exist  in  an  "  allotropic  "  state  which  is  not 
crystalline.  Sulphur  forms  some  very  notable  substances 
with  the  aid  of  other  elements.  Thus,  sulphuric  acid,  or 
"  oil  of  vitriol,"  is  an  oleaginous  liquid,  formed  by  three 
equivalents  of  oxygen,  one  of  sulphur,  and  one  of 
water.  Sulphuric  acid  forms,  with  various  other  sub- 
stances, certain  matters  termed  sulphates,  as  sulphate 
of  copper,  sulphate  of  magnesia,  sulphate  of  lime,  &c. 
It  takes  away  the  citric  acid  from  citrate  of  lime, 
seizing  on  the  latter  and  forming  sulphate  of  lime,  the 
citric  acid  being  thus  left  free.  The  termination  "ic" 
signifies  that  the  body  so  distinguished  has  more  oxygen 
than  one  distinguished  by  the  termination  "  ous  " — as 
sulphuric  acid  has  more  than  sulphurous  acid  has.  Sul- 
phurous  acid  is  formed  by  two  equivalents  of  oxygen  and 
one  of  sulphur.  It  produces  that  powerful,  suffocating 

*  As  to  what  a  crystal  is,  see  post,  p.  143. 


142  ELEMENTS   OF   SCIENCE 

odour  we  experience  when  sulphur  is  burnt ;  various 
bodies  formed  by  it  in  conjunction  with  certain  other 
matters,  are  termed  sulphides. 

Phosphorus  can,  like  sulphur,  exist  in  two  distinct 
solid  states.  One  of  these  also  is  crystalline ;  when  in 
its  not  crystalline  state,  it  is  said  to  be  in  an  amorphous 
condition.  It  has  a  great  affinity  for  oxygen,  and 
readily  bursts  into  flame,  while  ordinarily  it  is  in  a  state 
of  slow  combustion  which  makes  it  luminous  in  the  dark. 
In  union  with  oxygen  it  forms  phosphorus  and  phos- 
phoric acid,  the  latter  containing,  of  course,  the  greater 
proportion  of  oxygen.  Phosphoric  acid  when  united 
with  other  substances  forms  what  are  called  phosphates, 
as,  e.g.,  phosphate  of  lime. 

Iodine  exists  in  sea-water.  When  pure  it  is  a  soft, 
opaque,  crystalline  solid,  of  a  bluish  black  colour  and 
with  a  metallic  lustre.  When  moderately  heated  it 
becomes  a  violet  coloured  vapour,  which  solidifies  again 
in  crystals.  It  has  a  strong,  disagreeable  odour  and 
taste,  and  gives  an  intense  blue  colour  to  a  solution  of 
starch.  It  unites  with  metals,  forming  what  are  called 
Iodides. 

Of  the  metals,  gold  and  silver  do  not  rust  (oxidise) 
by  exposure  to  the  air,  and  they,  with  platinum,  mer- 
cury and  copper,  are  often  found  pure,  or  in  their 
"  native"  state,  as  it  is  called. 

It  is  just  the  reverse  with  the  metals  potassium,* 
calcium,  aluminium,  and  also  sodium,  the  oxide  of 
which  is  soda.  Magnesium  oxidises  as  magnesia.  /Silicon, 
or  silicium,  unites  with  oxygen,  as  before  said,f  to  form 
silica — i.e.,  silicic  acid,  and  the  products  of  this  acid  with 
other  bodies  are  termed  silicates.  Slate,  much  of  what 

*  See  ante,  p.  132.  f  See  ante,  p.  131. 


THE   NON-LIVING  WORLD  143 

we  call  clay,  with  granite,  quartz  and  various  other 
stones,  are  formed  of  "  silicates." 

Arsenic  is  a  metal  of  a  steel-gray  colour  and  consider- 
able brilliancy,  and  forms  with  oxygen  arsenious  and 
arsenic  acid. 

Iron  is  the  most  abundant  and  widely  diffused  of  all 
metals,  but  is  rarely,  if  ever,  met  with  pure.  It  is  found 
in  various  combinations,  or  "iron  ores"  The  natural 
magnet,  before  spoken  of,*  is  such  an  ore  in  the  form  of  a 
crystalline  oxide.  Carbonate  of  iron  mixed  with  various 
proportions  of  earthy  matters  forms  alone  one-third  of 
the  iron  ore  of  Great  Britain.  Iron  and  sulphur,  or  iron 
pyrites,  also  exists  in  enormous  quantity.  There  are 
also  chlorides  of  iron.  Steel  consists  of  iron  united  with 
carbon. 

We  have  spoken  of  certain  bodies  being  "  crystalline," 
which  means  that  they  are  made  up  of  crystals,  large 
and  small.  Now  a  crystal  is  a  solid  mineral  substance 
of  a  definite  geometrical  figure,  being  bounded  by  sur- 
faces, or  faces,  which  meet  so  as  to  form  sharp  edges 
and  angles.  The  angles  formed  by  these  faces  are 
characteristic  of  different  crystalline  substances,  though 
there  is  no  constancy  as  to  the  size  of  the  crystals,  or 
the  proportionate  size  of  their  several  faces.  Snow  is 
a  very  familiar  example  of  a  crystalline  body,  and  is  one 
which  can  only  exist  as  such  at  a  low  temperature.  If  a 
crystal  be  suspended  in  water  which  holds  in  solution  as 
much  as  it  can  contain  of  the  same  material  as  that 
whereof  the  crystal  is  composed,  then  if  the  liquid  be 
evaporated,  fresh  solid  material  may  be  deposited,  from 
the  liquid,  upon  the  surface  of  the  crystal,  which  will 
thus  increase  in  size.  If  a  crystal,  so  suspended,  be 

*  See  ante,  p.  125. 


144  ELEMENTS   OF   SCIENCE 

mutilated  by  having  one  of  its  solid  angles  removed, 
such  injury  will  be  repaired  by  the  deposition  of  fresh 
material  from  the  liquid. 

Crystals  also  possess  the  power  of  thus  resuming  growth 
after  interruption  ;  and  there  appears  to  be  no  limit  to 
the  time  after  which  the  resumption  of  growth  may 
take  place.  A  crystal  may  also  undergo  great  internal 
changes,  and  may  be  almost  entirely  disintegrated,  yet 
if  a  small  portion  remains,  it  may  grow  and  perfect 
itself  again.  Two  crystals  of  different  substances  may 
grow  so  as  to  become  almost  inextricably  intermixed, 
each  of  them  preserving  its  individuality  and  growing 
according  to  its  own  laws  all  the  time.  Crystals  may 
shoot  out  in  an  arborescent  manner,  as  we  often  see  in 
the  "  frost "  (which  consists  of  crystals  of  ice)  on  a 
window-pane. 

Stones,  rocks,  and  other  substances  are  said  to  be 
"  crystalline  "  when  they  are  formed  of  minute  crystals 
aggregated  together — as  is  the  case  with  marble  and  (as 
before  noted)  with  one  state  of  sulphur.  Other  minerals 
may  be  of  similar  chemical  composition,  but  not  formed 
of  minute  crystals — as,  e.g.,  chalk,  and  one  of  the  solid 
states  of  sulphur.*  The  formation  and  growth  of  crys- 
tals evidently  takes  place  by  most  minute  particles, 
answering  to  the  "  molecules "  spoken  of  in  the  last 
chapter,  each  molecule  being  composed  of  "  atoms," 
according  to  the  "  atomic  theory."  It  is  supposed 
that  these  atoms  are  persistent,  indestructible,  and  indi- 
visible, as  well  as  unchangeable  both  in  weight  and 
volume.  It  is  also  supposed  that  they  are  separated  by 
interstitial  spaces,  void  save  that  they  are  occupied  by 
efcher.  The  increase  or  decrease  of  these  spaces  is  thus 

*  See  ante,  p.  141. 


THE   NON-LIVING   WORLD  145 

deemed  to  be  the  one  explanation  of  the  augmentation 
and  diminution  of  the  bulk  of  bodies.  Finally  the 
atoms  of  the  chemical  elements  are  supposed  to  be  of 
determinate  specific  gravities.  These  hypotheses  are  of 
the  greatest  value  for  investigating,  predicting,  and  pro- 
ducing chemical  changes  of  analysis  and  synthesis. 
There  is  no  need,  however,  to  esteem  them  as  more  than 
working  hypotheses,  still  less  to  deem  them  a  sufficient 
and  exhaustive  explanation  of  the  real  nature  of  bodies. 
Indeed  there  are  various  considerations  which  at  present 
absolutely  forbid  us  so  to  regard  them. 

We  have  seen  how  various  substances,  such  as  carbon, 
sulphur,  and  phosphorus,  may  exist  in  two  or  more  differ- 
ent states,  but  there  are  certain  others  which  can  be  made 
to  alternate  between  two  conditions  neither  of  which  is 
truly  crystalline  though  one  of  them  is  allied  to  the  latter 
state.  Thus  the  same  chemical  substance  may  sometimes 
exist  in  a  state  which  is  termed  crystalloid  and  at  other 
times  in  the  state  of  what  is  called  a  colloid. 

Substances  which  are  in  a  "colloidal  condition  " — i.e., 
are  "  colloids  " — are  jelly-like,  and  insoluble  in  water. 
They  readily  absorb  water  through  their  substance  and 
swell,  while  they  will  also  readily  yield  it  up  again  by 
evaporation. 

Crystalloids  are  not  merely  the  reverse  of  all  this,  but 
are  specially  remarkable  for  their  diffusibility  ;  while 
colloids  can  hardly  diffuse  themselves  at  all  through  the 
substance  of  other  colloids. 

Substances  can  often  be  made  to  pass  from  the  crys- 
talloid to  the  colloidal  condition  by  adding  a  minute 
quantity  of  some  substance,  such  as  an  alkaline 
carbonate.  As  an  example  of  a  substance  which  will 
alternately  exist  in  these  two  states,  may  be  mentioned 
that  known  as  peroxide  of  iron. 

K 


146  ELEMENTS   OF   SCIENCE 

There  is  also  a  peculiar  action  of  liquids  which  may 
here  be  mentioned.  If  two  liquids  of  different  densities 
are  placed  within  a  vessel  so  that  they  are  separated  by 
a  median  porous  partition,  then  a  portion  of  each  liquid 
will  pass  through  the  partition,  but  more  of  the  less 
dense  liquid  will  pass  through  it  than  of  the  other. 
The  consequence  is  that  if  the  level  of  the  two  liquids 
be  at  first  the  same  on  each  side  of  the  partition,  then 
the  level  of  the  denser  liquid  will  rise,  while  that  of  the 
less  dense  liquid  will  sink.  This  process  of  fluid  trans- 
ference is  called  "  osmosis,"  and  it  is  facilitated  if  the 
partition  be  itself  a  colloidal  substance. 

We  must  now  return  from  this  digression  (which  has 
arisen  from  what  it  was  necessary  to  say  concerning 
crystals)  and  consider  a  little  further  what  are  the  solid, 
liquid,  and  aeriform  bodies  which  compose  this  earth. 

Limestone,  marble  and  chalk,  all  consist  of  carbonate 
of  lime*  and  have  been  produced  by  the  chemical  union 
of  lime  and  carbonic  acid.  If  sulphuric -acid  be  poured  on 
any  of  the  three  substances,  or  if  small  pieces  of  them 
be  placed  in  a  solution  of  sulphuric  acid,  bubbles  will  be 
given  off — there  will  be  effervescence.  This  is  due  to 
the  acids  changing  places.  The  sulphuric  acid  unites 
with  the  lime,  or  "  base,"f  and  the  carbonic  acid,  which 
is  normally  a  gas,  is  set  free — hence  the  effervescence. 
Other  acids — e.g.,  strong  vinegar — will  produce  a  similar 
effect.  Soil,  stones,  and  rocks  which  can  be  thus  acted 
on  are  called  calcareous.  Soil,  stones,  and  rocks,  where 
flint  or  silica  plays  the  part  which  Jime  plays  in  the 
calcareous  rocks,  are  termed  silicious.  Such  are  ala- 
baster, slate,  sand  and  sandstone  rocks.  Acids  have  no 
effect  upon  them.  Silicious  crystals  are  extremely  hard, 

*  See  ante,  p.  140.  t  See  ante,  p.  134. 


THE   NON-LIVING   WORLD  147 

and  quartz,  or  "  rock  crystal,"  is  one  of  the  commonest 
of  them.  Rarer  ones  are  rubies,  emeralds,  sapphires, 
topazes,  amethysts,  opal  and  the  substance  hydrophane, 
before  referred  to.*  The  most  brilliant  of  crystals,  dia- 
monds, are,  as  before  said,t  formed  of  carbon,  and,  of 
course,  are  neither  silicious  nor  calcareous.  Great  crystal- 
line masses  of  rock-salt  are  found  in  many  places. 

Grranite  consists  of  an  accumulation  of  crystals  of  three 
kinds  intermixed — namely,  quartz,  and  two  silicates  of 
alumina :  mica  and  feldspar.  Gneiss  is  a  highly  crystal- 
line rock,  composed  of  a  feldspar  with  mica  and  quartz. 

Porphyry  "and  basalt  are  allied  to  granite.  It  has 
been  found  by  experiment  that  such  rocks  can  be 
rendered  liquid  at  very  high  temperatures,  and  liquid 
rocks  of  such  kinds  exist  naturally  in  the, form  of  the 
lavaj  which  is  emitted  from  burning  mountains  or 
volcanoes. 

Our  atmosphere,  the  aeriform  envelope  of  the  earth, 
or  air,  is  not  like  water,  a  substance  resolvable  into 
gases,  chemically  combined,  but  is  a  mixture  of  gases 
and  vapours.  About  one-fifth  part  of  it  consists  of 
oxygen  and  almost  all  the  rest  of  nitrogen.  Carbonic 
acid  is  always  present  in  small  but  varying  quantities, 
as  a  general  rule  about  five  volumes  of  it  to  10,000 
volumes  of  air. 

There  is  also  some  ammonia  and  a  certain  quantity  of 
the  vapour  of  water.  The  amount  of  this  aqueous  vapour, 
however,  varies  greatly,  as  it  must  do  from  what  we  have 
already  seen  §  respecting  the  conversion,  by  heat,  of  liquid 
water  into  vapour  or  steam,  and  its  condensation,  at  a 
lower  temperature,  into  its  liquid  condition  once  more. 

*  S«e  ante,  p.  103.  t  See  ante,  p.  140. 

\  See  |*>«£,  p.  163.  §  See  ante,  pp.  86  and  87. 


148  ELEMENTS   OF   SCIENCE 

Air  has  lately  been  reduced,  by  Professor  Dewar,  to  a 
liquid  less  blue  than  liquid  oxygen. 

The  hotter  the  air,  the  greater  the  amount  of  aqueous 
vapour  it  can  contain,  and  vice  versa.  The  maximum 
quantity  which  air  contains  at  50°  F.  is  about  T|^  of  its 
weight,  but  at  82°  air  will  contain  ^  of  its  weight. 

If  air,  containing  much  aqueous  vapour,  be  suddenly 
cooled,  the  latter  is  thereby  forced  to  condense  itself 
into  particles  of  liquid  water,  which  may  appear  as  mist, 
cloud,  rain,  or  dew.  A  familiar  example  of  such  con- 
densation may  be  seen  when  a  decanter  of  iced  water  is 
brought  into  a  hot  room;  then  aqueous  vapour  will 
immediately  condense  upon  its  exterior. 

Dew  is  occasioned  by  the  radiation  *  of  heat  from  the 
earth's  surface  which,  when  the  sky  is  clear,  i.e.,  when 
there  are  no  clouds  to  reflect  it  back  again,  rapidly  cools 
that  surface,  and  so  forces  the  air  immediately  in  con- 
tact with  it,  to  condense  its  vapour  and  part  with  it  in 
the  form  of  dew.  Dew  does  not  fall,  but,  as  it  were, 
grows  upon  the  surface  it  coats,  just  as  on  the  surface 
of  the  decanter  of  iced  water  above  mentioned.  Hoar 
frost  is  vapour  frozen  into  crystals  of  ice. 

Since  the  warmer  the  air,  the  greater  the  amount  of 
aqueous  vapour  it  may,  but  by  no  means  must,  contain, 
it  follows  that  the  greater  amount  of  cooling  air  can 
stand  without  shedding  its  dew,  the  drier  it  must  be — 
the  less  the  proportion  of  aqueous  vapour  in  it.  In 
England  it  rarely  needs  30°  of  cooling,  but  in  some  hot 
climates  it  may  need  more  than  twice  this  amount. 

The  main  essential  characters  of  air,  in  as  far  as  it  is  a 
gaseous  body,  have  already  been  stated, t  as  well  as  the 
downward  force  it  exercises,  and  the  consequent  compres- 

*  See  ante,  p.  96.  t  See  ante,  pp.  78  and  147. 


THE   NON-LIVING   WORLD  149 

sion  and  greater  density  of  its  lower  strata,  owing  to  the 
pressure  on  them  of  the  air  above.  The  atmosphere  is 
supposed  to  form  a  layer  over  the  earth's  surface  of 
probably  between  forty  and  fifty  miles  in  thickness.  At 
the  sea  level,  100  cubic  inches  of  air  at  60°  F.  weigh 
about  30  grains,  but  at  an  elevation  of  20,000  feet  the 
pressure  on  them  would  be  diminished  one-half;  for  there 
is  as  much  air  in  the  lower  3 \  miles  of  the  atmosphere  as 
in  all  the  superior  portion.  The  weight  of  the  atmosphere 
at  any  spot  is  tested  by  the  barometer.* 

As  has  been  pointed  out,f  the  sun's  rays  hardly  at 
all  raise  the  temperature  of  the  atmosphere ;  it  is 
warmed  by  the  earth's  surface,  which  is  itself  heated 
by  the  rays  passing  to  it  through  the  air.  Then  the 
superincumbent  mass  of  air,  becomes  gradually  warmed 
by  convection,!  and  so  currents  upwards  and  down- 
wards are  produced.  Now  the  earth's  surface  is  very 
unequally  heated,  that  of  tropical  lands  being  vastly 
hotter  than  at  the  arctic  regions,  and  the  air  being 
most  expanded  by  the  warmer  surface  will  rise  to  a 
greater  elevation  above  it,  than  elsewhere. 

But  no  fluid,  either  liquid  or  aeriform,  can  heap  itself 
up.  It  must  overflow,  and  then  it  will  immediately 
be  pressed  upon  by  a  rush  of  colder  and  therefore 
heavier  air.  Thus  it  is  winds  are  produced,  which 
are  of  the  greatest  utility  in  lessening  extremes  of  tem- 
perature. There  is  a  constant  rise  of  warm  air  from  the 
hottest  regions  of  the  earth,  which  then  flows  north- 
wards and  southwards  at  a  high  altitude  towards  the 
poles,  while  lower  currents  of  cold  air  rush  simul- 
taneously towards  the  equator.  This  is,  on  a  gigantic 


*  See  ante,  p.  82.  t  See  ante,  p.  98. 

J  See  ante,  p.  95. 


1 50  ELEMENTS   OF   SCIENCE 

scale,  what  takes  place,  on  a  minute  scale,  in  every  room 
where  there  is  a  fire,  or  which  is  in  any  way  unequally 
heated.  But  the  currents  towards  the  poles  after  a  time 
become  so  much  cooler,  while  the  equatorially  rushing 
air  becomes  so  much  warmer,  that  they  have  generally 
been  supposed  to  change  places  at  about  latitude  30°. 
Thence  the  air  from  the  equator  generally  forms  the 
lower  current,  till  it  approaches  the  pole,  where  it  again 
rises  amidst  the  irregularities  of  wind  known  as  "  polar 
gales  "(Fig.  22). 

FIG.  22. 


The  action  of  different  degrees  of  heat  has  great  effect 
in  determining  the  motion  of  the  winds,  but  most  con- 
spicuous effects  are  also  produced  by  another  cause,  as 
follows :  The  earth,  as  every  schoolboy  knows,  revolves 
on  its  axis  from  west  to  east  once  in  every  twenty-four 
hours.  Now,  just  as  the  body  of  every  traveller  in  a 
carriage  or  a  boat,  participates  in  the  velocity  of  the 
vehicle  which  carries  him,*  so  the  atmosphere  more  or 
less  fully  participates  in  the  velocity  of  that  part  of  the 
earth's  surface  it  covers.  But  from  the  globular  shape  of 

*  See  ante,  p.  58. 


THE   NON-LIVING   WORLD  151 

the  earth  it  is  evident  that  while  at  the  equator  the  sur- 
face of  the  earth  has  a  rotatory  motion  of  1042  miles  an 
hour,  that  of  a  circle  very  near  one  of  the  poles  would 
travel  at  the  rate  of  only  ten  miles  an  hour,  and  others  still 
nearer  at  a  less  and  less  rate.  Therefore  polar  currents 
(from  the  equator,  towards  the  poles)  must  acquire  an  east- 
ward direction,  as  their  velocity  east  will  grow  more  and 
more  in  excess  of  that  of  each  tract  of  the  earth's  surface 
they  pass  over.  On  the  other  hand,  the  currents  from  the 
poles  towards  the  equator  will  more  and  more  fall  below 
the  velocity  of  each  part  of  the  rotating  earth  they  succes- 
sively come  to.  They  will  therefore  lag  behind  it,  and  so 
appear  to  blow  in  a  westerly  direction  and  this  constantly. 
These  currents  constitute  the  trade  winds  of  the  Northern 
and  Southern  Hemispheres.  Near  the  equator  they 
become  neutralised,  and  the  heated  air  ascends,  and  so 
we  have  an  equatorial  band  of  calms  and  occasional 
storms  between  the  north  and  south  trade  winds.  The 
trade  winds  are  modified  by  the  form  of  the  continents 
they  traverse,  while  they  disappear  north  and  south  of 
latitude  30°,  They  disappear  by  giving  place  to  the 
variable  winds  of  the  temperate  regions  with  which  we 
are  familiar,  and  the  conditions  determining  which  are 
too  complex  to  be  further  noticed  here,  the  reader  being 
referred  for  such  knowledge  to  works  on  Meteorology. 

The  winds  of  the  Indian  Ocean  known  as  "  monsoons  " 
are  modifications  of  the  trade  winds  due  to  the  influence 
of  vast  masses  of  land.  Land  and  sea  breezes  are  due  to 
the  more  equable  temperature  of  the  sea  and  the  more 
ready  heating  and  cooling  of  the  surface  of  the  land. 
During  the  day  the  tendency  is  for  the  air  over  the 
cooler  sea  to  come  in  as  a  sea  breeze,  and  replace  the 
ascending  current  of  air  produced  by  the  action  of  the 
sun's  heat  on  the  land.  After  sunset,  on  the  contrary,  the 


152  ELEMENTS   OF   SCIENCE 

shores  becoming  cooler  than  the  sea,  we  have  an  opposite 
effect,  a  breeze  from  land  to  sea.  Hill  and  valley  breezes 
also  exist,  partly  due  to  mountain  summits  receiving  more 
heat  by  day,  and  radiating  it  far  more  readily  by  night 
than  do  the  lowlands,  arid  partly  to  colder  and  therefore 
heavier  air  rolling  down  hill. 

Rotatory  storms,  hurricanes,  and  typhoons  may  have  a 
diameter  of  four  or  five  hundred  miles.  Such  move- 
ments are  not  so  many  transfers  of  the  mass  of  air  itself, 
but  are  rotatory  movements  of  great  velocity  trans- 
mitted through  its  particles.  They  are  supposed  to  be 
occasioned  by  a  rapid  movement  of  ascent  communicated 
to  air  by  some  very  heated  spot  of  the  earth's  surface,  such 
movement  taking  place  through  air  either  relatively  at 
rest  or  moving  in  a  contrary  direction.  This  would  be 
sufficient  to  occasion  an  incipient  vortex  which  may  be 
compared  with  the  conical  vertices  before  considered*  as 
occurring  in  water.  Rotatory  storms  wander  about  with 
a  movement  of  translation  which  is  slow  when  compared 
with  the  enormous  rapidity  of  rotation,  which  may  be 
more  than  ninety  miles  an  hour.  These  aerial  vortices 
proceed  obliquely  north  and  south  from  the  region  of  the 
equator,  turning  from  west  to  east,  while  their  move- 
ment of  translation,  in  the  northern  hemisphere,  is  west- 
ward till  they  have  passed  the  region  of  the  trade  winds, 
then  they  turn  eastwards. 

There  is  an  instrument  for  measuring  the  wind's  force 
(anemometer  or  anemoscope)  consisting  of  an  upright 
U-shaped  tube,  containing  a  little  water,  with  one  end 
bent  horizontally  so  as  to  face  the  wind.  A  scale  for 
registering  the  height  of  the  water  is  placed  between 
the  two  limbs  of  the  upright  tube,  the  water  being,  of 

*  See  ante,  p.  74. 


THE   NON-LIVING  WORLD  153 

course,  of  the  same  height  in  each  limb  when  there  is  no 
pressure.  Then  when  the  horizontal  part  of  the  tube  is 
made  to  face  the  wind,  its  pressure  will  be  registered  by 
the  amount  of  elevation  thus  produced,  of  the  water,  in 
the  opposite  limb  of  the  tube.  A  gentle  breeze  will 
support  0.025  inches  of  water,  a  brisk  gale,  0.5.  A  storm 
will  sustain  3  inches,  and  a  violent  hurricane,  9  inches. 

There  are  certain  elevations  and  depressions  which 
affect  the  whole  aerial  envelope  of  the  globe,  but  these 
will  be  noticed  in  connection  with  "  Ocean  Tides."  * 

Water  is  commonly  spoken  of  as  being  "  fresh  "  or 
"salt"  water.  In  fact,  however,  it  always  contains  a 
greater  or  less  quantity  of  foreign  substances  dissolved 
in  it,  but  not,  of  course,  chemically  united  with  it.  In 
the  first  place  water  —  except  water  that  has  been  boiled 
—  contains  a  considerable  quantity  of  air  mixed  up 
within  it,  and  rain-water  gathers  in  its  descent,  some  of 
the  air's  soluble  constituents,  including  carbonic  acid  and 
ammonia.  The  water  of  each  river  necessarily  contains 
some  of  the  salts  of  the  springs  which  feed  it,  and  it  also 
contains  the  matters  which  it  dissolves  out  from  the 
material  which  it  meets  with  in  its  course.  Amongst 
the  more  noteworthy  ingredients  it  thus  acquires,  are 
carbonate  of  lime  and  flint  in  a  state  of  solution.  Thus 
the  Thames  carries  past  Kingston  daily  not  less  than  1514 
tons  of  solid  substance  (mainly  derived  from  calcareous 
formations  of  Berkshire,  Oxfordshire,  and  Gloucester- 
shire), which  includes  more  than  1000  tons  of  carbonate 
of  lime.  Sea-water  notoriously  contains  a  great  deal  of 
salt,  with  other  chlorides  and  sulphates,  and  with  some 
ammonia  and  iodine. 

There  are  currents  in  the  ocean  due  to  differences  of 


,  p.  182. 


154  ELEMENTS   OF   SCIENCE 

temperature,  as  we  have  seen  there  are  in  the  air. 
From  the  two  extremely  cold  regions  of  the  globe — the 
Arctic  and  Antarctic  regions — cold  ocean  currents 
extend,  in  variously  modified  ways,  towards  the  equator, 
while  warm  currents  diverge  north  and  south  from  the 
equatorial  region  towards  the  poles. 

As  every  one  is  aware,  there  is  a  diurnal  ebb  and  flow 
of  the  ocean  which  is  known  as  "  the  tides,"  but  their 
consideration  will  be  deferred*  till  some  words  have 
been  said  about  the  celestial  bodies,  as  otherwise  they 
could  not  be  understood. 

The  distribution  of  the  earth's  dry  land  has  great 
effect  on  these  currents  and  on  the  climates  of  the  world 
generally.  The  greatly  preponderating  mass  of  dry 
land  is  situated  north  of  the  equator,  and  is  divisible 
into  two  unequal  sections — (i)  one  consisting  of  the 
continent  of  America,  and  the  other  (2)  of  the  con- 
tinents of  Europe  and  Asia,  with  Africa.  The  latter 
section  may  be  regarded  as  one  great  whole  because, 
though  Africa,  but  for  the  Isthmus  of  Suez,  would  be 
an  island,  the  Mediterranean  and  Red  Seas,  which 
divide  it  from  Europe  and  Asia,  are  very  insignificant 
tracts  of  water  compared  with  the  great  oceans,  and 
each  of  these  is  bounded  at  its  outlet  by  a  very  narrow 
strait.  These  two  great  sections  descend  southwards  in 
three  prolongations,  dividing  the  earth's  immense  marine 
envelope  of  salt  water  into  three  oceans.  The  American, 
or  New  World,  section,  after  becoming  extremely 
narrowed  towards  the  Isthmus  of  Panama,  rapidly 
spreads  out  again  into  an  enormous  mass  of  land  ex- 
tending east  and  west,  and  then  gradually  narrows  to  Cape 
Horn,  which  reaches  southwards  to  the  56°  of  south 

*  Seeposf,  p.  182, 


THE  NON-LIVING  WORLD  155 

latitude.  Thus  America  divides  the  Atlantic  from  the 
Pacific  Ocean.  The  old-world  section  of  the  earth  sends 
southwards  two  prolongations.  The  first  of  these  is 
formed  by  the  African  continent,  which  terminates  at 
the  Cape  of  Good  Hope,  and  does  not  quite  attain  34°  of 
south  latitude.  The  second  prolongation  is  formed  by 
Asia  where  it  ends  in  the  Malay  Peninsula,  but  which 
does  not  quite  reach  the  equator.  It  may,  however,  be 
said  to  be  continued  onwards  by  the  mass  of  large  and 
small  islands  which  constitute  the  Indian  Archipelago, 
and  by  the  vast  quasi-continent  of  Australia,  which 
extends  to  a  little  beyond  south  latitude  39°.  The 
Atlantic  ocean  bounds  Africa  and  Europe  on  the  west, 
while  the  eastern  shores  of  Asia  and  Australia  are  washed 
by  the  Pacific,  the  southern  prolongations  of  Africa  and 
Asia  enclose  between  them  the  third,  or  Indian  ocean, 
into  the  middle  of  the  North  of  which  Hindostan  pro- 
jects, running  downwards  till  it  ends  at  Cape  Comorin 
in  a  little  over  8°  of  north  latitude. 

With  respect  to  the  volume  of  the  earth's  marine 
liquid  envelope  compared  with  that  of  the  land  above 
its  surface,  it  would  seem  that  the  former  is  more  than 
forty  times  in  excess  of  the  latter.  Also  more  than  two 
thirds  of  the  surface  of  the  globe  is  covered  by  water, 
which,  at  the  poles,  assumes  the  form  of  ice.  There 
is  a  much  more  extensive  ice-cap  on  the  South  Pole 
than  the  North  Pole,  and  no  one  knows  how  much  land 
the  south  ice- cap  may  cover. 

The  globe  can  easily  be  mapped  out  in  such  a  manner 
that  one  hemispherical  map  shall  show  very  little  besides 
water  except  the  southern  ice-cap.  For  if  we  make  a 
map  of  one  hemisphere,  taking  London  as  our  centre,  we 
shall  have  on  it  the  maximum  of  land,  while  on  the  oppo- 
site hemisphere  will  be  the  maximum  of  water  (Fig.  23). 


156 


ELEMENTS   OF   SCIENCE 


The  distribution  of  dry  land  is  thus  most  irregular, 
as  also  is  the  degree  to  which  the  shape  of  any  large 
portion  of  land  is  varied  by  deep  indentations  in,  and 
far-reaching  prolongations  from,  its  shores. 

Besides  the  British  Isles  and  Iceland,  those  islands 
most  desirable  here  to  note  (with  a  view  to  succeeding 
chapters)  are  Ceylon,  Sumatra,  Java,  Borneo,  Celebes, 
the  Philippine  and  Japan  Islands;  the  small  islands 
Bali,  Lambok,  and  Timor  ;  Madagascar,  with  its  distant 
outliers,  Mauritius  and  Bourbon — all  in  the  Indian 
Ocean ;  the  Canaries,  the  Cape  de  Verde  Islands,  Ascen- 


FIG.  23. 


sion,  and  St.  Helena ;  the  West  Indian  Islands  and 
Trinidad — all  in  the  Atlantic  Ocean;  the  Galapagos, 
Sandwich,  and  Society  Islands,  Fiji,  New  Caledonia,  the 
Solomon  Islands  ;  New  Zealand,  New  Guinea — all  in 
the  Pacific  Ocean ;  and  finally  the  Moluccas  and  Aru 
Islands,  and  Tasmania,  which  last,  as  it  were,  prolongs 
Australia  to  the  south.  Some  of  these  are  noteworthy 
as  being  separated  by  very  deep  water  from  land  adjacent, 
while  others  are  remarkable  as  rising  in  groups  from  a 
surface  but  little  submerged,  and  separated  by  no  great 
depth  from  an  adjacent  continent, 


THE   NON-LIVING  WORLD  157 

The  greater  oceans  contain  abysses  which  sink  much 
deeper  below  the  ocean's  level  than  any  mountains 
ascend  above  it.  With  these  complex  conditions  of  shore 
and  sea-bottom,  it  is  no  wonder  that  ocean  currents 
become  thereby  variously  diverted  from  the  courses  they 
would  take  were  they  affected  by  nothing  but  varia- 
tions of  temperature.  Nevertheless  difference  of  tem- 
perature is  the  great  cause  of  their  existence,  while  one 
of  their  most  noteworthy  effects  is  the  great  change  they 
can  produce  in  land  climates.  Thus  while  cold  currents 
sweeping  down  from  the  Greenland  seas,  carry  ice  and 
cold  water  southwards  along  the  east  coast  of  America, 
to  40°  of  north  latitude,  the  equatorial  current  (proceed- 
ing westwards  across  the  Atlantic  and  northwards  to 
the  Gulf  of  Mexico)  and,  its  prolongation,  the  Gulf 
Stream  (extending  north-eastwards  from  the  Mexican 
Gulf)  carry  warmth  with  their  waters  into  western  Europe 
and  over  the  North  Cape.  Did  a  belt  of  land  extend 
between  Britain  and  Greenland,  so  as  to  intercept  the 
passage  of  this  warm  stream  (as  the  land  bounding 
Behring  Straits  stays  the  passage  northwards  of  the 
warm  currents  of  the  Pacific  Ocean),  we  should  then  see 
the  mountains  of  Scandinavia  (like  those  in  Greenland 
in  nearly  the  same  degree  of  latitude)  permanently 
covered  with  ice  and  snow. 

The  elevations  of  the  land — mountain  chains — exert 
various  effects  on  currents  of  air — the  winds — analogous 
to  those  produced  by  the  form  of  coasts  on  ocean 
currents.  Mountains  are  sometimes  very  lofty,  the 
highest  in  the  world,  those  of  the  Andes,  rise  close  on 
30,000  feet,  while  Himalayan  peaks  exceed  27,000. 
The  direction  of  mountain  chains  is  also  most  influential. 
No  line  of  mountains  running  east  and  west  in  North 
America,  checks  the  descent  of  polar  winds  to  the  Gulf 


158  ELEMENTS   OF   SCIENCE 

of  Mexico.  The  great  chain  of  the  Andes  runs  from 
north  to  south  very  near  the  west  coast  of  South  America. 
Very  different  would  be  the  effect  of  the  trade  winds 
did  the  Andes  bound  the  eastern  instead  of  the  western 
coast  of  that  continent. 

These  various  modifications  of  aerial  and  ocean 
currents,  cause  the  temperature  of  different  places  of 
the  earth's  surface  and  atmosphere  and  the  degrees  of 
their  humidity  (in  other  words,  their  climates)  to  vary 
independently  of  their  degree  of  latitude,  i.e.,  their 
distance  from  the  equator.  Different,  indeed,  are  the 
climates  of  mild  Cornwall  and  frigid  Newfoundland 
(though  the  latter  is  south  of  the  former),  and  of  Bordeaux 
and  Halifax  (in  Nova  Scotia)— both  of  nearly  the  same 
degree  of  latitude.  Lines  which  connect  places  of  similar 
temperatures  are  termed  isothermal  lines.  They  are 
much  and  irregularly  curved,  and  therefore  widely  differ 
from  the  circles  which  mark  degrees  of  latitude. 

The  evaporation  of  water  over  the  earth's  surface 
causes  the  atmosphere,  as  before  pointed  out,*  to  contain 
a  greater  or  less  quantity  of  aqueous  vapour,  sometimes 
even  to  become  saturated,  that  is,  to  contain  the  greatest 
quantity  it  can  possibly  hold.  The  rapid  condensation 
of  this  vapour  produces  rain. 

When  air  laden  with  vapour  blows  from  districts  with 
a  cooler  climate  to  another  which  is  warmer,  it  acquires  a 
still  greater  capacity  for  aqueous  vapour,  and  the  result 
is  that  the  .clouds  (which,  as  before  said,  are  masses  of 
minute  particles  of  water),  being  dissipated  into  steam, 
vanish  altogether. 

On  the  other  hand,  when  winds  saturated  with  vapour 
pass  into  a  cold  region,  torrents  of  rain  may  result. 

*  See  ante,  p.  148. 


THE   NON-LIVING   WORLD  159 

Such  is  the  case  when  the  trade  winds,  laden  with 
vapour  from  the  Atlantic,  begin  to  ascend  the  slopes  of 
the  Andes,  the  summits  of  which — even  at  the  equa- 
tor— are  clothed  with  perpetual  snow  at  a  height  of 
sixteen  thousand  feet.  At  such  an  altitude,  and  at  so 
low  a  temperature,  the  vapour  assumes  the  solid  form  of 
crystalline  water — i.e.,  snow.  The  limit  at  which  such 
snow  can  form  itself  on  mountains — called  the  snow-line 
— descends  as  we  recede  on  either  side  from  the  equator. 
In  the  Swiss  Alps  it  is  at  about  from  8500  to  8000  feet, 
but  descends  to  5000  feet  on  the  Norwegian  mountains. 
In  the  Arctic  and  Antarctic  regions  it  gains,  apart  from 
the  influence  of  winds,  the  sea-level.  The  mere  cold 
of  very  great  altitudes  keeps  lofty  mountain-tops  con- 
stantly below  32°  F.  In  the  equatorial  regions,  heat 
diminishes  i°  for  e^ery  333  feet  of  ascent,  and  therefore 
above  15,700  feet  it  must  freeze  every  night.  But  this 
lowering  of  the  snow-line  does  not  by  any  means  take 
place  with  regularity,  as  the  previously  mentioned  curva- 
ture of  isothermal  lines  would  alone  be  enough  to  show. 
Thus,  Captain  Cook  found  snow  at  the  sea  level  in  the 
island  of  South  Georgia  between  54°  and  55°  of  south  lati- 
tude. This  is  not  more  distant  south  from  the  equator 
than  Durham  is  distant  to  the  north  of  it.  The  piling  up 
of  snow  by  continual  deposits  on  lofty  mountains,  causes 
the  mass  to  force  its  way  slowly  down  the  highest  valleys, 
through  the  action  of  gravity.  Gradually  solidifying,  it 
forms  glaciers,  and  they  accommodate  themselves  to  the 
various  capacities  of  the  depressions  through  which  they 
travel,  by  breaking  themselves  up.  But  their  broken  frag- 
ments re-adhere  with  such  speed  that  the  mass  often 
seems  as  if  it  squeezed  through  narrows  without  be- 
coming fractured.  On  their  road,  they  score  and  furrow 
the  rocks  they  press  against,  and  are  powerful  enough  to 


160  ELEMENTS   OF   SCIENCE 

scoop  out  large  excavations,  so  deepening  the  depressions 
in  the  mountain  sides  and  in  the  valleys  which  they 
traverse.  The  length  of  Swiss  glaciers  is  sometimes 
twenty  miles,  their  breadth  occasionally  two  or  three 
miles,  and  their  depth  600  feet.  They  melt  slowly  as 
they  descend,  the  water  flowing  in  tunnels  beneath  them, 
and  issuing  from  under  ice  arches  at  their  lower  extremity. 
Masses  of  rocks,  or  boulders,  and  many  stones  are  carried 
along  by  them,  accumulating  at  the  glacier's  lower  ter- 
mination, such  accumulations  being  known  as  moraines. 

In  high  latitudes,  great  masses  of  glacier  will  break  off 
into  the  sea  and  float  away  to  warmer  climes,  as  icebergs, 
carrying  with  them  large  masses  of  rock  and  boulders 
with  a  large  quantity  of  stones  and  mud.  They  have 
been  seen  so  large  as  to  be  many  miles  in  circumference 
and  300  feet  high.  Such  a  mass  must  be  vast  indeed, 
seeing  that  for  every  cubic  foot  above  the  sea's  surface 
there  must  be  eight  cubic  feet  below  it. 

But  the  condensation  which  appears  occasionally  as 
snow,  but  generally  as  rain,  takes  place  very  unequally 
over  the  earth's  surface.  The  tropics  are  most  abundantly 
watered,  parts  of  Brazil  receiving  annually  as  much 
as  270  inches  of  rain,  and  Cherra  Poonjee,  in  Assam, 
500  inches.  On  the  east  of  the  Andes,  however, 
there  is  a  narrow  tract  of  land  which  is  rainless  because 
the  constant  western  winds  are  drained  of  their  water 
as  they  pass  over  the  snow-capped  mountains.  That 
great  desert,  the  Sahara,  of  Northern  Africa,  is  rainless, 
because  the  moist  winds  and  clouds  it  may  receive  from 
the  Mediterranean  find  in  it  not  a  condenser  but,  on 
aecount  of  its  heat,  a  vapouriser,  which,  as  before  said,* 
makes  clouds  vanish.  The  great  tableland  of  Gobi,  in 

*  See  ante,  p.  158. 


THE   NON-LIVING   WORLD  161 

Central  Asia,  is  a  rainless  desert  because  the  vaporous 
winds  from  the  Indian  Ocean  are  drained  of  their  mois- 
ture ere  they  reach  it  over  the  Himalaya,  while  the 
mountains  of  China  drain  the  humid  winds  which  pass 
to  it  from  the  Pacific. 

It  is  evident  that  districts  far  from  the  sea,  and  desti- 
tute of  mountains,  must  possess  less  aqueous  vapour  in 
their  atmosphere  than  others  in  the  vicinity  of  the  ocean, 
of  seas,  or  of  large  lakes.  This  alone  must  make  the 
climate  of  South  America  more  humid  than  are  the 
central  regions  of  the  Old  World  which  are  so  much  more 
distant  from  the  shores  of  the  ocean. 

It  is  from  rain  that  all  the  rivers  of  the  world  have 
their  origin.  For  the  springs  from  which  so  many  arise 
are  but  the  outcrop  of  the  rain  which  has  penetrated  the 
soil  till,  having  come  to  an  impervious  stratum,  it  can 
descend  no  longer,  but  must  issue  forth  at  the  lowest 
level  of  the  upper  surface  of  such  impervious  stratum. 
In  rain,  all  fresh-water  lakes  also  have  their  origin,  since 
they  are  produced  by  impediments  in  the  rapid  progress 
of  rivers.  There  are,  however,  other  lakes — such  as 
the  intensely  salt  Dead  Sea  —  which  have  another 
origin,  being  remnants  left  behind  by  seas  which  have 
receded. 

The  largest  rivers  are  in  the  New  World ;  the 
Amazon  runs  a  course  of  3000  miles,  and  drains 
1,500,000  square  miles  of  country.  The  Mississippi  of 
North  America  is  almost  if  not  quite  as  long,  but 
drains  a  less  extent  of  land.  The  Yangtse-kiang  of 
China  runs  a  course  of  2500  miles;  the  Nile,  the  Ganges, 
and  the  Indus  are  also  of  great  extent. 

Water  in  the  form  of  rain,  rivers,  streams  and  sea 
waves,  is  continually  modifying  the  earth's  surface,  by 
destroying  its  more  elevated  parts.  This  modifying 


162  ELEMENTS   OF  SCIENCE 

action  is  largely  aided  by  ice,  for,  as  we  have  seen,*  water 
expands  when  it  freezes,  and  thus  it  must  enlarge  any 
cracks  and  fissures  into  which  it  may  have  made  its  way 
and  frozen.  By  these  means  the  land  is  being 
continually  torn  down  and  carried  off  to  be  deposited 
either  in  estuaries,  or  at  the  mouths  of  rivers,  or  in  the 
bed  of  the  ocean.  The  mass  of  matter  thus  carried  to 
the  sea  by  some  of  the  largest  rivers  is  enormous.  It  has 
been  calculated  that  the  Ganges  carries  down  every  year 
as  much  land  as  could  be  carried  down  by  730,000  ships, 
each  of  1400  tons  burthen.  The  substances  carried 
down  by  the  Mississippi  have  formed  at  the  mouth  of 
that  river,  in  the  Gulf  of  Mexico,  a  deposit  extending 
over  an  area  of  30,000  square  miles,  and  is  known  to  be, 
at  least  in  some  parts,  several  hundred  feet  in  thickness. 
A  deposit  thus  formed  at  a  river's  mouth  is  generally 
more  or  less  triangular  in  shape,  on  which  account  it  is 
called  a  delta,  from  its  resemblance  in  shape  to  the 
Greek  letter  so  named.  It  is  only  when  seas  are  more 
or  less  enclosed  (as,  e.g.,  the  Gulf  of  Mexico  and  the 
Mediterranean),  or  where  the  ocean  currents  are  weak, 
that  the  transported  materials  are  deposited  so  as  to 
form  deltas.  Egypt  largely  consists  of  the  delta  formed 
by  the  Nile,  and  it  has  been  calculated  that  not  less 
than  17,000  years  have  been  required  for  its  formation. 
Deposits  of  this  kind  carried  down  by  rivers  into  fresh- 
water lakes,  also  form  "  deltas  "  therein. 

The  eroding  action  of  water  is  notorious.  When  the 
gradient  of  a  river  is  considerable  (as  is  commonly  the 
case  in  the  upper  courses  of  rivers),  its  excavating  action 
is  also  considerable,  and  if  such  a  gradient  be  maintained 
to  the  coast,  the  river  will  excavate  a  deep  channel 

*  See  ante,  p.  91. 


THE   NON-LIVING   WORLD  163 

bordered  by  high  land  to  its  mouth — as  in  the  Tyn 
and  the  Tweed.  The  excavation  by  a  river  of  its  own 
valley  may  leave  here  and  there,  high  up  in  sheltered 
positions,  accumulations  of  drifted  materials,  marking 
the  level  at  which  the  river  flowed  at  successive  earlier 
periods. 

Every  child  who  has  the  opportunity  of  examining  an 
undulating  sandy  surface  after  violent  rains,  may  see 
clearly  both  the  eroding  and  the  depositing  action  of 
water.  It  needs  but  a  much  prolonged  action  of  that 
kind  to  cause  profound  modifications  of  the  earth's 
surface.  There  is  no  mountain  which  is  not  almost 
incessantly  being  in  this  way  rendered  more  steep  and 
precipitous,  and  thus  the  whole  land  of  the  globe 
constantly  tends  to  be  washed  down  by  rivers,  and 
spread  out  beneath  the  surface  of  the  sea.  But  the 
finer  debris  of  the  land  carried  down  incessantly  into  the 
sea  by  rivers,  is,  when  the  action  of  the  river-water 
ceases,  caught  up  by  the  great  marine  currents  and 
swept  to  places  more  or  less  widely  distant  and  out  of 
the  reach  of  tidal  action. 

The  lowering  of  the  earth's  surface  by  the  wear  and 
tear  of  water  is  more  or  less  counterbalanced  by  a  slow, 
or  rapid,  upheaval  of  other  parts  of  its  surface  through 
volcanic  action.  The  number  of  burning  mountains — 
active  volcanoes — in  the  world  may  be  estimated  at 
about  300,  and  some  of  these  give  forth  vast  quantities 
of  lava.*  For  example,  in  the  Island  of  Ha wai  a  burning 
deluge  of  lava  broke  forth  in  1840  from  the  crater  of 
Kilauea ;  it  spread  from  one  to  four  miles  wide  and 
reached  the  sea  in  three  days,  at  a  distance  of  thirty 
miles,  and  for  fourteen  days  it  plunged,  in  a  vast  fiery 


*  See  ante,  p.  147. 


164  ELEMENTS   OF   SCIENCE 

cataract  a  mile  wide,  over  a  precipice  fifty  feet  high 
into  the  ocean. 

Volcanoes  are  very  unequally  distributed  over  the 
earth's  surface.  One  of  the  most  considerable  volcanic 
regions  is  that  in  the  Andes  (between  Quito  and  Chili), 
and  there  is  another  in  Mexico.  A  volcanic  region  of 
very  great  extent  passes  from  the  Philippines  through 
the  Moluccas,  Timor,  Lombok,  and  Bali  into  Java  and 
Sumatra.  Volcanoes  have  been  known  to  resume  their 
activity  after  a  quiescence  of  centuries. 

The  slow  upheaval  and  depression  of  different  parts  of 
the  earth's  surface  have  been  proved  by  direct  observa- 
tions. The  Andes  have  been  rising  century  after  century 
at  the  rate  of  several  feet,  while  the  region  of  the  eastern 
Pampas  has  risen  but  a  few  inches.  The  land  of  Scan- 
dinavia, towards  North  Cape,  rises  above  five  feet  in  a 
century,  and  very  many  other  instances  could  easily  be 
adduced  of  slow  secular  elevation.  Soundings  often  give 
good  reason  to  suppose  both  that  some  rather  distant  lands 
once  formed  part  of  an  adjacent  continent,  as  also  that 
islands,  which  by  their  proximity  to  some  mainland 
might  be  supposed  to  have  been  previously  united  to  it, 
have  not  really  been  so,  but  have  only  become  nearer  to 
it  through  a  recent  elevation  of  the  mainland's  coast. 
But  however  considerable  such  changes  may  here  and 
there  have  been,  it  seems  probable  that  the  great  oceans 
and  continents  have  been  permanent  save  for  more  or 
less  considerable  modifications  of  their  margins  and 
boundaries. 

The  science  which  treats  of  the  structure  of  the  earth, 
and  the  causes  which  have  brought  about  the  present 
condition  of  its  surface,  is  the  science  of  geology.  The 
earth's  crust,  mainly  composed  of  the  mineral  substances 
before  noticed,  is  made  up  of  superimposed  masses  of 


THE  NON-LIVING  WORLD  165 

them,  such  superimposed  masses  being  called  strata. 
These  strata  consist  of  various,  generally  more  or  less 
horizontal,  layers  of  different  materials,  and  are  generally 
composed  of  consolidated  mud  which  has  been  deposited 
(in  the  way  described)  in  fresh  or  salt  water  lakes,  or  in 
deep  or  shallow  seas.  But  not  all  rocks  are  due  to  the 
agency  of  water.  Many  masses  have  been  ejected  in  a 
molten  state  from  volcanoes,  and  solidified  either  on  the 
land's  surface  or  beneath  the  sea,  and  therefore,  in  the 
latter  case,  under  great  pressure.  Rocks  which  are  thus 
due  to  volcanic  agency  are  called  igneous  rocks.  Those 
of  them  which  have  been  formed  under  the  sea  are  called 
plutonic ;  otherwise  they  are  termed  volcanic.  Igneous 
rocks  are  not  generally  stratified,  and  they  may  be  of  all 
ages.  Some,  like  those  which  form  part  of  Snowdon 
and  Cader  Idris,  are  very  old.  Others,  like  those  of 
Etna,  and  those  which  cover  Herculaneurn,  are  relatively 
quite  recent.  Deposits  may  have  undergone  four  kinds 
of  change  :  (i)  they  may  have  undergone  a  mere  process 
of  drying  (as  with  sands) ;  or  (2)  drying  accompanied  by 
pressure  (as  with  sandstone) ;  or  (3)  with  chemical  action 
in  addition  (as  with  highly  crystalline  rocks  like  that 
called  gneiss*) ;  or  (4)  a  change  may  have  been  produced 
by  infiltration.  Thus  rocks  may  be  infiltrated  by  iron, 
lime,  or  silica,  producing  ferruginous,  calcareous,  and 
silicious  sandstones  and  conglomerates,  which  last  are 
sometimes  called  "  pudding  stones,"  and  consist  of  frag- 
ments of  rock  cemented  together. 

The  strata  thus  forming  the  crust  of  the  earth  are 
supposed  to  be  from  sixteen  to  eighteen  miles  thick ;  but 
no  boring  has  yet  extended  to  even  one  mile  in  depth, 
and  indeed  has  scarcely  exceeded  3000  feet.  The  total 

*  See  ante,  p.  147. 


1 66  ELEMENTS   OF   SCIENCE 

depth,  therefore,  is  purely  a  matter  of  inference  from 
the  arrangement,  superposition,  and  inclination  of  the 
different  strata,  as  seen  at  or  near  the  surface. 

After  penetrating  a  moderate  distance,  the  tempera- 
ture of  the  earth's  interior  has  been  found  to  augment, 
the  greater  the  depth  explored,  at  the  rate  of  i°  Fahren- 
heit, sometimes  for  every  45  feet  and  sometimes  for  every 
70  feet  approximately. 

The  various  strata  of  which  the  earth's  crust  is  com- 
posed were,  of  course,  deposited  at  successive  times,  and 
the  time  of  the  deposition  of  each  is  called  its  "  period  " 
or  "  epoch."  But  for  subsequent  disturbance,  the  most 
ancient  strata  would  always  be  deepest,  and  superposition 
would,  in  all  cases,  plainly  indicate  relative  novelty.  As 
it  is,  we  have  often  to  examine  carefully  in  order  to 
discover  the  real  order  of  deposition,  but  this  once 
discovered,  depth  is  equivalent  to  age,  and  vice  versa. 
The  uppermost  and  most  recent  accumulations  of  sands, 
clays  and  gravels,  form  what  are  called  the  "recent 
deposits,"  and  these  are  not  counted  as  forming  any  part 
of  the  proper  geological  strata,  and  are  not  represented 
in  ordinary  geological  maps,  but  are  there  disregarded. 
The  strata  beneath  these  recent  deposits  are  classed  in 
three  great  groups,  belonging  respectively  to  three  great 
epochs.  The  deepest  and  most  ancient  group  comprises 
the  strata  called  Primary  or  Palceozoic.  The  second  or 
middle  group  of  strata  is  called  Secondary  or  Mesozoic. 
The  uppermost  and  least  ancient  group  consists  of  strata 
called  Tertiary  or  Cainozoic.  The  "recent  deposits" 
really  belong  to  this  last-mentioned  group,  and  we  may 
be  said  to  be  still  living  in  the  Tertiary  period,  which  has 
succeeded  the  only  two  earlier  periods  of  which  as  yet  we 
have  evidence — namely,  the  secondary  and  the  primary 
periods  or  epochs. 


THE   NON-LIVING  WORLD 


167 


FIG.  24. 


PLEISTOCENE 
(250  ft.) 


PLIOCENE 

(100  ft.) 
MIOCENE 

(125  ft.) 

EOCENE 

(2,000  ft.). 


Bronze,  and  NcolitUic  Ages 
Peat,  Alluvium,  Loess 
Valley  Gravels,  Brickearths 
Cave-deposits 
:  ;vaches 

1'alarolitliVc  Age 
Boulder  Clay  and  Gravels 


Norfolk  Forest-bed  Series 
Norwich  and  Ked  Crags 
Coralline  Crag  (l)icstian) 

(Eningcn  Beds  Freshwater,  <tc. 
Fluvio-marino  Series  (Oligoccne) 

aMB-.}*-— •»* 


CRETACEOUS 
(7,000  ft.) 

NEOCOMIAN 


Maestricht  Beds 

Chalk 

Upper  Greensand 

Gaulc 

Lower  Greensand 

\VeaIdcn 


JURASSIC 

(3,000  ft.) 


TEIASSIO 

(3,000ft.) 


Purbeck  Beds 
Portland  Beds 
Kiinnicridge  Clay  (Solenhof 
Corallian  Beds 
Oxford  Clay 
Great  Oolite  Series 
nferior  Oolite  Series 


PEHMIAN  or         I 
DYAS  < 

(500  to  3,000  ft.)  ( 

CARBONIFEROUS  \ 

(12,000  ft.) 

DEVONIAN  &  OLD  ( 
BED  SANDSTONE  K 

fa.noo  to  10.000  ft.) 


Upper  Old  Ked  Sandstone 
Lower  Old  Red  Sandstone 


SILURIAN 

(3,000  to  5,000  ft.) 

ORDOVICIAN 

(5,000  to  8,000  ft.) 

CAMBRIAN 

(20,000  to  30,000  ft.) 


Ludlow  Series 
\Veiilock  Scries 
Llandovcry  Series 
May  Hill  Series 
Bala  and  Caradoc  Scries 
Llandeilo  Series 
Llanvirn  Scries 
Arenijr  and  Skiddaw  Series 
Tremadoc  Slates 
LinRula  Klacs 
Mdini.sn  Series 
Harlecli  and  Longmynd  K> 


EOZOIC- 
RCH^EAN 
(30,000  ft.) 


Pebidian,  Arvonian,  and  Ditnct 
Laurcntiaa 


(After  Dr.  Woodward,  F.R.S.) 


i68  ELEMENTS   OF   SCIENCE 

Each  of  these  three  great  groups  of  rocks  is  made  up 
of  a  certain  number  of  subordinate  groups  of  strata  or 
formations  grouped  in  systems.  Thus  the  Palaeozoic,  or 
Primary  rocks,  are  made  up  of  the  Eozoic-archcean 
(including  the  Laurentian  formation),  Cambrian,  Ordo- 
vician,  Silurian,  Devonian,  Old  Red  Sandstone,  Car- 
boniferous and  Permian  systems.  The  Laurentian  rocks 
are  very  largely  developed  in  Canada,  and  are  some 
30,000  feet  in  thickness.  The  Cambrian  rocks  are 
from  15,000  to  20,000  feet  thick,  and  are  well  seen 
in  the  Longmynds  of  Shropshire,  and  near  Bangor, 
Harlech,  and  St.  Davids  in  Wales.  The  Silurian 
strata  (sandstones,  clays,  limestones,  and  igneous  rocks) 
are  of  very  great  thickness,  and  form  a  large  part  of 
Wales,  the  lake  district  of  England,  Southern  Scotland, 
and  some  parts  of  Ireland.  The  Devonian  system  is 
exemplified  in  Devon  and  Cornwall,  and  the  Old  Bed 
Sandstone  rocks  of  Ireland,  Scotland,  and  Wales.  The 
Carboniferous  system  includes  the  Carboniferous 
limestone  and  the  Coal  measures.  The  latter  consists  of 
seams  of  coal  and  layers  of  sandstone  and  slate;  such 
alternations  indicating  oscillation  of  level.  The  Permian 
system  is  of  moderate  thickness,  and  mainly  consists 
of  magnesian  limestone  associated  with  many  slates  and 
beds  of  conglomerate.  In  England  it  is  chiefly  found 
skirting  the  coal-fields  from  Durham  to  Derbyshire.  The 
Mesozoic  or  Secondary  rocks,  are  made  up  of  Triassic, 
Jurassic,  Neocomian,  and  Cretaceous  systems ;  the  first 
(Trias}  — which  includes  strata  known  as  the  "  New  Red 
Sandstone  " — extends  in  England  from  Devon  to  York- 
shire, and  is  largely  developed  in  Cheshire.  The  Jurassic 
rocks  contain  all  formations  from  the  Lias  and  the  Oolite. 
to  the  Purbeck  beds.  The  Lias  extends  from  Lyme  Regis, 
obliquely  north-east  to  Whitby.  The  Oolite  also  extends 


THE  NON-LIVING  WORLD  1^9 

between  the  north-east  and  south-west  of  England.    To 
the   upper   portion    of   the   Jurassic   rocks   belong   the 
Solenhofen  slates  of  Bavaria.     The  Cretaceous  and  Neo- 
comian  systems  include  the  Wealden,  the  lower  and  upper 
Gault,  and  the  Chalk.     The  Wealden  is  well  seen  in  the 
Greensand,  the  south-east  of  England,  where  (in  Kent, 
Surrey,  Sussex,  and  the  Isle  of  Wight)  it  is  considered  to 
represent  the  delta  of  a  large  ancient  river.     The  Chalk 
formation   ranges   from   Lyme   Regis  to  Flamborough 
Head,   and    also    forms    both    our   North   and   South 
Downs.    It  and  the  Maestricht  beds  terminate  the  series 
of  Mesozoic  formations,  and  a  great  break  exists  between 
it  and  the  Tertiary  formations  which  follow.     The  break 
between   them  seems  to   be   partially  bridged   over   in 
North- Western  America  by  certain  beds  known  as  the 
"  Lignite    Series."     The    Cainozoic,    or   Tertiary   rocks 
consist   of    three    systems  —  the   Eocene,   the    Miocene, 
and  the  Pleiocene.     Eocene   rocks  underlie   both  Paris 
and   London,    and   form    very    important    deposits   in 
North   America,      The    Miocene    formation    is    widely 
distributed  in  Europe  and   the  North  American  Con- 
tinent,   but    is   very   slightly    represented   in   Britain. 
The  igneous  rocks  which  form  the  Giant's  Causeway, 
the  Island  of  Staffa,  of  Mull  and  others,  belong,  how- 
ever, to  the  group.     The  Pleiocene  formation  is  exten- 
sively  distributed   in   Europe,    Asia,    and   the    United 
States.      In    England   it  is   represented   by  the   Nor- 
folk and  Suffolk   "Crag."     The  later,  Pleistocene,  rocks 
— the  so-called   Quaternary  strata — include  the  deposits 
found  in  ancient  caves  in  Europe  and  those  thrown  down 
during  what  is  known  as  the  Glacial  Epoch.     That  such 
a  period  of  intense  cold  prevailed  over  Northern  and 
Central  Europe  and  the  greater  part  of  North  America, 
in  geologically  recent  times,  is  shown  by  the  evidence  of 


1 70  ELEMENTS   OF   SCIENCE 

prodigious  glaciers,*  which  appear  to  have  scooped  out 
valleys,  and  scored  the  surface  of  hill  and  dale  in 
those  regions.  Blocks  of  stone  or  "  boulders  "  are  often 
found  scattered  about  there,  and  seem  to  have  been 
transported  by  ice,  sometimes  for  very  great  distances. 

The  various  strata  which  thus  form  the  crust  of  the 
earth  contain,  in  different  degrees  of  rarity  or  abundance, 
certain  objects  which  are  known  as  "fossils."  Amongst 
the  mass  of  materials  carried  down  by  rivers  and 
deposited  along  their  course  or  in  their  deltas,  or  at  the 
bottom  of  the  sea,  are  numerous  relics  of  that  kind. 
When  such  a  relic  becomes  entombed,  it  often  happens 
that  particle  by  particle  of  its  substance  is  replaced, 
particle  by  particle,  by  mineral  matter  (ferruginous, 
calcareous,  or  silicious)  till  we  have  a  complete  represen- 
tation— technically  called  a  " pseudomorph" — of  the 
original  in  such  new  material. 

There  are  five  kinds  of  fossils  : — 

(i)  Objects  preserved  unchanged,  or  little  changed  so 
that  they  retain  the  greater  part  of  their  own  mineral 
material  matter;  (2)  substitutes  or  "pseudomorphs";  (3) 
moulds,  i.e.,  deposits  which  present  the  impressions  made 
by  objects,  all  other  evidences  of  which  have  disappeared. 
Thus  impressions  of  hailstones  made  in  a  soft  surface  of 
mud,  have  often  been  preserved  by  subsequent  delicate 
layers  of  deposit.  Then,  the  whole  having  become 
hardened,  the  shape  of  such  impressions  when  laid  bare 
by  the  geologist,  may  show  us  to-day  the  direction  in 
which  the  wind  blew  when  those  hailstones  fell  at  some 
unimaginably  distant  period  of  past  time ;  (4)  casts  of 
moulds,  i.e.,  solid  matter  which  has  taken  the  place  of 
whatever  bodies  may  have  produced  the  moulds  and  then 

*  See  ante,  p.  159. 


THE   NON-LIVING   WORLD  171 

disappeared — such  would  be  the  solid  matter  filling  up 
the  hollows  formed  by  the  hailstones  and  so  replacing 
them  ;  (5)  casts  of  hollow  structures,  i.e.,  mineral  matter 
which  has  filled  cavities  in  the  interior  of  fossils  and  so 
formed  internal  casts  (as  "  moulds "  are  external  casts) 
of  fossils.  For  further  information  about  the  earth's 
crust  the  reader  is  referred  to  special  works  on  geology. 

Having  now  considered  the  effects  of  heat,  motion,  and 
chemical  changes  upon  the  globe  as  a  whole,  it  remains  to 
speak  of  the  influence  exercised  upon  it  by  electricity  and 
magnetism,  as  well  as  of  the  external  sources  of  its  light 
and  heat,  and  the  effects  produced  upon  it  by  them 
through  gravity. 

We  have  seen  *  that  the  motion  of  either  electricity  or 
magnetism,  circulating  round  an  axis,  develops  the 
other  force  along  that  axis.  Now  there  is  a  constant 
flow  of  electric  currents  around  the  earth  from  east  to 
west,  and,  besides  this,  the  unequal  heating  of  the 
surface  of  the  globe  in  each  twenty-four  hours  has  its 
necessary  electrical  consequences.! 

The  result  of  the  circulation  of  electricity  round  the 
globe  is  to  make  the  world  itself  a  huge  magnet  with 
two  opposite  magnetic  poles.  These  poles  are  not  far 
from  the  poles  of  the  earth's  rotation — the  north  and 
south  poles.  The  northern  magnetic  pole  is  near 
Hudson's  Bay,  and  the  opposite  one  is  amidst  the 
Antarctic  ice ;  but  their  positions  slowly  change  and 
revolve  round  the  earth  from  east  to  west. 

It  is  the  presence  of  these  poles  which  has  enabled 
navigation  to  be  aided  by  the  magnetised  needle  of  "the 
mariner's  compass."  This  magnetic  needle  is  so  placed 
on  a  pivot  that  it  can  turn  freely  in  any  direction,  and 

*  See  ante,  p.  127.  t  See  ante,  p.  124. 


172  ELEMENTS   OF   SCIENCE 

it  constantly  points  towards  the  magnetic  north  pole — or 
rather  its  long  axis  always  coincides  with  the  line  join- 
ing the  magnetic  poles — unless  it  be  made  to  deviate  by 
some  local  magnet,  or  mass  of  iron  in  its  vicinity.  But 
as  the  magnetic  poles  do  not  coincide  with  the  earth's 
poles  of  rotation,  and  as  the  imaginary  circles  or 
"  meridians "  (real  as  drawn  on  maps)  which  mark 
degrees  of  longitude,  all  pass  through  the  poles  of 
rotation  (the  geographical  north  and  south  poles),  the 
long  axis  of  the  magnet  will  not  coincide  with  such 
"  meridians "  along  any  great  circle.  Theoretically, 
there  ought  to  be  one  such  circle  of  coincidence,  but, 
owing  to  the  fact  that  in  the  globe  (as  in  other  natural 
magnets)  magnetism  is,  more  or  less,  irregularly  dis- 
tributed, the  line  of  coincidence  is  also  irregular.  This 
circle  extends  from  near  Hudson's  Bay,  through  the 
United  States,  Cuba,  Jamaica,  and  Brazil,  to  the  South 
Magnetic  Pole,  whence  it  is  continued  on  through 
Australia,  China,  and  Siberia  to  the  North  Magnetic 
Pole,  near  Hudson's  Bay,  whence  we  started.  The 
further  the  magnetic  needle  may  diverge  from  this  line, 
the  greater,  of  course,  will  be  its  divergence  from  a 
geographical  meridian,  and  such  divergence  is  called  its 
variation.  The  magnetic  needle,  while  constantly  point- 
ing towards  its  pole,  undergoes  slight  changes,  daily, 
monthly,  and  yearly,  while  every  now  and  then  it 
undergoes  sudden  and  irregular  disturbances,  indicating 
what  are  called  magnetic  storms,  and  these  seem  to 
extend  over  the  whole  earth. 

The  magnetic  needles  may  be  exactly  balanced 
horizontally,  and  yet  able  to  lower  one  end,  or,  as  it  is 
technically  termed,  to  dip.  The  nearer  such  a  needle 
is  brought  towards  either  magnetic  pole,  the  more  it  will 
dip,  and  at  either  such  pole  it  will  be  vertical,  while 


THE   NON-LIVING   WORLD  173 

along  a  line  equidistant  from  both,  it  will  be  horizontal. 
The  "  dip  "  of  the  needle  is  subject,  like  its  variation,  to 
daily,  monthly,  and  yearly  changes,  as  well  as  to  sudden 
storms. 

The  external  sources  of  the  world's  heat  and  light  are, 
of  course,  the  "  heavenly  bodies  " — the  sun,  moon,  and 
stars,  the  study  of  which  constitutes  the  science  of 
astronomy. 

The  earth,  as  every  one  now  knows,  is  not  only  a 
sphere,  revolving  on  its  axis  daily,  but  also  accomplishes, 
together  with  its  satellite,  the  moon,  an  annual  revolu- 
tion round  the  sun.  It  is  therefore  a  planet,  i.e.,  one  of 
those  various  other  spheres  which  also  revolve  round  the 
sun,  together  with  their  satellites ;  and  which  planets, 
with  certain  comets,  and  clouds  of  more  or  less  relatively 
minute  bodies,  called  meteoroids,  constitute  a  planetary, 
or  solar,  system.  This  system  again  is  but  one  of  many 
systems  of  suns  (it  may  be  with  or  without  attendant 
planets)  which  make  up,  together  with  some  dark  globes 
and  masses  of  gases  or  vapours — termed  nebulce — the 
visible  sidereal  universe. 

The  various  bodies  of  this  universe,  which  vary 
immensely  as  to  size,  are  continually  changing  their 
relative  positions  according  to  the  mechanical  laws  of 
dynamics,  already  noted,  and  the  force  of  gravity. 
These  bodies  are  all  material  bodies,  and  we  have  seen  * 
that  all  such  are  (by  gravity  acting  between  them)  drawn 
together  directly  as  their  masses  and  inversely  as  the 
squares  of  their  distances.  It  is  the  study  of  the 
relative  movements  of  the  heavenly  bodies  which  has 
revealed  to  us  the  universality,  so  far  as  we  have  been 
able  to  test  it,  of  the  law  of  gravitation. 


*  See  ante,  p.  66, 


174  ELEMENTS   OF   SCIENCE 

The  grand  result  of  this  energy  is  that  the  planets  of 
our  system,  and  doubtless  those  of  other  systems,  revolve 
round  suns  or  central  bodies,  in  ellipses,  variously 
attended  by  satellites,  which  in  turn  revolve  around 
their  respective  planets.  In  some  distant  systems  there 
may  be  more  than  one  sun.  Thus  for  our  purpose  we  may 
consider  the  universe  as  divided  into  two  parts  :  (i)  The 
sun  with  its  attendant  bodies,  i.e.,  the  solar  system ;  and 
(2)  The  rest  of  the  universe  which  can  by  any  means  be 
made  visible  to  us — nebulae,  and  all  the  bodies  called 
"  fixed  stars  "  because  they  have  for  us  no  obvious  move- 
ment. We  class  the  latter,  for  convenient  description, 
in  groups  termed  constellations,  such  as  that  of  the 
Great  Bear  (familiarly  known  as  Charles's  Wain)  and 
others.  Such  groups,  however,  have  no  natural  con- 
nection but  are  only  associated  together  on  account  of 
their  conspicuousness  and  apparent  proximity. 

Our  own  solar  system  is  rushing  at  the  rate  of  ten 
thousand  miles  every  half-hour  in  the  direction  of  the 
constellation,  known  as  Lyra,  and  no  doubt  all  the 
other  suns  or  fixed  stars  are  similarly  in  motion, 
although  their  great  distances  make  such  movements 
inappreciable.  The  known  universe,  or  cosmos,  is  made 
up  of  bodies  variously  composed  of  solid,  -  liquid,  or 
gaseous  matter,  and  these  bodies  differ  greatly  in  density, 
some,  as  before  mentioned,  being  but  masses  of  vapour, 
the  "  nebulae." 

The  cosmical  bodies  shine  either  by  self-emitted  light 
(as  does  our  sun  and  the  variously  distant  stars)  or  by 
reflected  light,  as  do  the  planets  and  satellites  of  our 
solar  system  and,  probably,  multitudes  of  planets  of 
other  systems,  though  some  planetary  bodies  themselves 
may  be  very  faintly  self-luminous. 

All  our  heat  is  derived  from  the  sun,  and  also  almost 


THE   NON-LIVING   WORLD  175 

all  our  light,  since  the  moon  and  planets  reflect  their  light 
on  us,  the  light  of  the  distant  self-luminous  stars  being 
quite  insignificant  in  comparison  with  the  direct  and  re- 
flected solar  light.  The  surface  and  atmosphere  of  the  sun 
form  a  region  of  intense  energy  and  heat.  Just  as  aqueous 
vapours  ascend  from  the  surface  of  the  earth  and,  after 
condensation,  fall  back  on  it  as  showers  of  rain,  so  in 
the  sun  metallic  vapours  are  continually  ascending,  to 
be  condensed  and  fall  down  in  showers  of  red-hot  metal, 
amidst  flames  of  hydrogen,*  thousands  of  miles  high. 

Now,  as  we  have  seen,t  light  travels  at  the  enormous 
speed  of  186,330  miles  in  a  second,  through  whatever 
intervenes  between,  and  connects  together,  all  the  plane- 
tary and  stellar  bodies.  The  hypothetical  substance, 
ether,:j:  before  noted  as  the  medium  of  light,§  must,  if 
indispensable  for  luminous  energy,  be  universally  dif- 
fused wherever  light  is  transmitted.  Wherever  light 
can  travel,  there  must  then  be  ether ;  and  light  can 
travel  through  every  known  interval,  and  through  the 
most  perfect  vacuum  which  we  can  make.  Therefore, 
neither  can  we  make  a  real  vacuum,  nor  can  there  be 
any  between  us  and  the  most  distant  visible  star.  The 
distance  from  us  of  the  nearest  visible  fixed  star  (Alpha 
cenlauri)  being  about  272,000  times  greater  than  that  of 
the  sun — which  itself  is  about  92,700,000  miles  away — 
the  time  which  light  must  take  in  passing  from  it  (the 
nearest  fixed  star)  to  our  eyes  is  three  years.  Even  the 
light  of  the  sun  takes  eight  minutes  to  come  to  us,  and 
that  of  the  most  distant  known  planet,  Neptune,  takes 
five  hours.  The  light  of  the  most  distant  visible  stars 
probably  takes  centuries  to  reach  us,  so  that  in  what  we 

*  See  ante,  p.  139.  f  See  ante,  p.  103. 

J  See  ante,  p.  93.  §  See  ante,  p.  102. 


176  ELEMENTS   OF   SCIENCE 

see  of  them  we  only  see  what  existed  more  than  one 
hundred  years  ago. 

This  great  and  uniform  speed  of  light  combined  with 
the  motion  of  the  earth,  causes  what  is  known  as  the 
aberration  of  light.*  It  is  common  to  all  the  heavenly 
bodies,  and  causes  them  all  to  appear  a  little  out  of  their 
true  place.  While  the  light  is  travelling  from  any  star 
towards  an  observer,  the  observer  himself  is  being  simul- 
taneously carried  along  with  great  rapidity  by  the  earth, 

The  result  is  that  if  he  directs  his  telescope  exactly 
towards  a  star,  the  light  which  enters  his  instrument 
will  strike  the  side  of  it  before  it  can  reach  his  eye. 
This  has  therefore  to  be  allowed  for,  and  the  instrument 
accordingly  directed  a  little  in  advance  of  the  object 
observed,  just  as  a  sportsman  has  to  shoot  in  front  of  a 
running  hare,  to  allow  for  its  change  of  place  during  the 
passage  of  a  shot. 

The  di&tances  and  sizes  of  the  nearer  heavenly  bodies, 
and  the  size  of  the  earth  itself,  have  been  ascertained  by 
the  application  of  geometrical  principles,  and  mainly 
that  one  which  teaches  us  that  two  triangles,  however 
different  in  size,  are  in  other  respects  exactly  similar  to 
each  other  provided  the  angles  of  one  are  the  same  as 
the  angles  of  the  other. 

Thus  if  we  require  to  know  the  exact  distance  of  some 
object  on  that  side  of  a  wide  river  which  may  be  oppo- 
site to  us,  we  may  ascertain  it  as  follows  :  We  must 
select  two  spots  A  and  B  on  our  side,  and  measure  the 
length  of  the  straight  line  between  them.  Then  plant- 
ing ourselves  at  A  we  must  observe,  with  an  instrument 
made  for  that  purpose,  a  distant  object,  0,  and  ascertain 
the  angle  formed  by  the  line  AB  with  that  which 

*  Before  referred  to,  p.  103. 


THE   NON-LIVING  WORLD 


177 


passes  from  our  eye  at  A  to  O.  Next  we  must  plant 
ourselves  at  B,  and  similarly  observe  the  angle  formed 
by  AB  with  a  line  from  B  to  0.  Thus  we  may  easily 
obtain  a  triangle  which  will  enable  us  to  tell  the  dis- 
tance of  0.  To  do  this  we  must  draw  on  paper  a 
straight  line  ab,  and  from  its  two  ends  draw  two  other 
lines  such  that  the  angle  formed  at  b  by  one  of  them 
shall  be  the  same  as  the  angle  we  observed  at  the  point 
B,  while  the  angle  formed  at  a  shall  be  equal  to  that 
we  observed  at  the  station  A.  Let  these  lines  be  ax 


and  ay  respectively ;  then  if  we  prolong  them  enough 
they  will  meet  at  some  point  p.  Then  the  small  triangle 
on  paper,  apb,  will  be  similar  to  (i.e.,  equiangular  with) 
the  large  triangle  formed  by  the  straight  line  AB  and 
the  two  lines  respectively  extending  from  A  and  B  and 
meeting  at  the  distant  object  0.  Therefore  the  length 
of  AB  must  bear  the  same  proportion  to  ap  as  the 
line  AB  bears  to  AO  and  by  measuring  the  actual 
lengths  of  the  three  lines  of  the  triangle  apb  and  that 
of  the  line  AB,  it  is  easy  by  the  simple  arithmetical 
process  known  as  "  the  rule  of  three,"  to  ascertain  the 


178  ELEMENTS   OF   SCIENCE 

dimensions  of  the  two  lines  AO  and  BO  and  so  the 
distance  of  the  object  0. 

By  an  extension  of  this  principle  to  the  observation  of 
the  angles  formed  by  lines  passing  from  any  one  spot 
on  the  earth's  surface  to  some  fixed  star  (a  process  which 
cannot  be  explained  here),  it  has  been  ascertained  that  the 
earth  is  a  globe  with  a  circumference  of  24,840  miles. 
We  can  ascertain  this  because  the  distance  of  the  fixed 
stars  is,  as  we  have  seen,  so  enormous  that  they  remain 
for  our  observations  always  practically  in  one  relative 
place. 

Having  ascertained  the  earth's  dimensions  we  can 
treat  its  diameter  as  we  before  supposed  the  two  ends  of 
the  measured  line  AB  to  be  treated;  and  so  ascertain 
the  angles  formed  by  it  with  lines  passing  from  its 
extremities  to  the  moon,  and  when  once  the  distance 
of  a  body  is  known,  we  can  readily  find  its  size  and  vice 
versa,  by  the  simplest  application  of  the  before-mentioned 
principle  of  "  similar  triangles." 

By  careful  observations  of  the  apparent  path  of  the 
planet  Venus  across  the  sun's  disc  (in  what  is  known  as 
the  transit  of  Venus),  as  seen  from  two  spots  on  the 
earth's  surface,  it  was  determined  in  1761  and  1769  that 
the  sun's  distance  from  the  earth  was  from  93,274,000 
to  96,432,000  miles.  This  being  ascertained,  it  became 
easy  to  ascertain  the  size  of  the  earth's  orbit,  which  then 
provided  an  enormously  larger  and  more  useful  base 
for  triangular  measurements.  Our  measured  line  AB 
might  now  be  taken  as  190,000.000  miles  (such  being 
the  diameter  of  the  earth's  orbit),  observations  from  the 
opposite  extremities  of  which,  as  to  the  angles  formed 
by  it  with  more  distant  heavenly  bodies,  served  for 
further  investigation  of  dimensions  and  distances.  But 
so  distant  are  the  fixed  stars  that  even  with  this 


THE  NON-LIVING  WORLD  ifg 

enormous  base,  the  amount  of  their  remoteness  remains 
unascertainable  save  in  some  thirty  instances,  as  (with 
these  exceptions)  they  present  no  appreciable  difference 
of  position,  or,  as  it  is  called,  no  parallax,  when  viewed 
from  opposite  points  of  the  earth's  orbit. 

The  sun  is  852,900  miles  in  diameter,  and  1,252,700 
times  the  volume  of  the  earth. 

Our  satellite,  the  moon — which  is  only  238,813  miles 
distant  from  us,  and  has  but  a  diameter  of  2,160  miles- 
circles  round  us  in  about  four  weeks  and  turns  once  on 
her  own  axis  during  each  such  revolution.  Therefore 
the  same  side  of  the  moon  is  ever  turned  towards  the 
earth.  The  so-called  changes  in  the  moon,  of  course, 
simply  result  from  the  different  amounts  of  her  surface 
which  are,  at  different  times,  illuminated  by  the  sun's 
rays.  Similar  changes  are  also  shown  by  the  planet 
Venus. 

The  moon  appears  to  be  devoid  of  both  air  and  water, 
or  if  such  substances  exist  there,  they  seem  to  have 
retreated  into  the  moon's  interior,  and  give  no  signs  of 
their  presence  on  its  much  scarred  surface. 

As  to  the  shape  of  the  paths  followed  by  the  earth  and 
the  other  planets  in  their  revolution  round  the  sun,  they 
follow  precisely  the  same  laws  as  regulate  any  body  so 
moving  round  another  that  it  cannot  fall  to  the  surface 
of  the  latter.  We  have  already  seen  *  that  any  body  pro- 
jected from  a  point  external  to  the  earth's  surface,  and 
with  a  certain  velocity,  would  be  constrained  to  revolve 
round  it  in  an  ellipse  and  that  its  radius  vector  must 
always  pass  through  equal  areas  in  equal  times  and  always 
in  the  same  plane.  This  is  the  precise  law  of  the  earth's, 
and  of  all  the  other  planets',  revolutions  round  the  sun. 

*  See  ante,  p.  65. 


i8o  ELEMENTS   OF   SCIENCE 

Every  planet,  moreover,  not  only  describes  an  elliptical 
orbit,  but  one  whereof  the  sun's  centre  is  one  of  the 
foci.  These  laws  were  discovered  by  Kepler,  who  also 
found  out  that  the  time  occupied  by  a  planet  in 
revolving  round  its  orbit  is  proportional  to  the  square 
root  of  the  cube  of  the  mean  (i.e.,  average)  diameter  of 
its  orbit.  The  times  (in  days)  which  the  different  planets 
take  so  to  revolve  are  :  Mercury,  88  ;  Venus,  225  ;  the 
Earth,  365;  Mars,  687  ;  Jupiter,  4333;  Saturn,  10,759; 
Uranus,  30,687;  Neptune,  60,181. 

As  to  the  relative  size  of  the  sun  and  planets,  if  the 
Earth  be  represented  by  a  pea,  Venus  will  also  be 
so  represented  ;  Mercury  by  a  grain  of  mustard  seed ; 
Mars  by  a  large  pin's  head,  Jupiter  by  an  orange, 
Uranus  by  a  cherry,  while  the  Sun  would  need  a  sphere 
4  feet  in  diameter  to  represent  it.  As  to  degrees  of 
density,  Mercury  is  about  twice  as  dense  as  the  Earth, 
which  itself  is  about  five  and  a  half  times  as  dense  as 
water.  Jupiter,  on  the  other  hand,  is  but  a  quarter  of 
the  density  of  our  globe. 

As  might  be  expected,  though  some  of  the  planets 
differ  greatly  from  the  earth  in  density  and  other 
physical  conditions,  there  is  a  substantial  resemblance 
between  them  which  is  sometimes  carried  very  far. 
Thus  our  nearest  neighbour — after  the  moon — the  planet 
Mars,  appears  to  be  so  like  our  earth  as  to  have  not  only 
its  tracts  of  land  and  water  but  also  caps  of  polar  ice. 

The  planets  of  the  solar  system,  with  their  satellites, 
move  round  the  sun  in  the  same  direction,  with  the 
exception  of  the  satellites  of  Uranus  and  the  solitary 
attendant  on  Neptune.  These  move  in  a  retrograde 
direction,  and  the  former  are  also  very  exceptional  in 
that  their  orbits  are  nearly  perpendicular  to  the  plane 
of  the  earth's  orbit. 


THE   NON-LIVING   WORLD  181 

The  planets,  like  the  earth,  revolve  on  their  axes  while 
they  go  round  the  sun,  and  their  satellites  revolve  round 
the  planets  they  attend  more  slowly  than  such  planets 
revolve  on  their  own  axes.  An  exception,  however, 
o'ccurs  in  the  case  of  the  planet  Mars,  one  of  the 
satellites  of  which  circulates  round  it  in  less  than  a 
third  of  the  time  that  planet  takes  to  revolve  on  its  own 
axis. 

Since  the  earth's  orbit  is  elliptical,  our  globe  must  be 
nearer  the  sun  at  one  time  (in  one  part  of  its  path)  than 
at  another.  It  is  furthest  from  the  sun  during  our 
summer  and  nearest  in  winter,  but  its  axis  slants  in  such 
a  manner  that  its  north  pole  inclines  towards  the  sun  in 
summer  and  away  from  it  in  winter.  Therefore  the 
earth's  northern  hemisphere  receives  the  sun's  rays  most 
directly  when  it  is  furthest  from  it,  and  least  so  when  it 
is  nearest  to  it.  This  is  why  our  summer  season  is  the 
warmest,  while  the  same  period  is  the  coldest  for  the 
globe's  southern  hemisphere.  In  spring  and  summer 
the  condition  is  intermediate,  hence  the  four  "  seasons." 

During  each  spring  and  autumn,  our  obliquely  inclined 
globe  is  for  a  short  time  in  such  a  position  that  the 
illuminated  half  of  its  surface  is  situated  symmetrically 
as  regards  the  poles.  This  is  the  period  of  the  equinoxes, 
or  of  equal  night  and  day  all  over  the  globe. 

As  the  northern  pole  becomes  more  and  more  inclined 
towards  the  sun,  its  daylight  is  prolonged  till  (e.g.  North 
of  North  Cape)  the  sun  never  sets,  while  in  winter  it 
never  rises.  The  opposite  condition  of  course  obtains 
at  the  Antarctic,  or  south  pole. 

The  circuit  described  by  the  earth  in  its  path  round 
the  sun  is  constantly  changing  to  a  small  degree.  It 
alternately  approximates  to,  and  diverges  further  from, 
a  truly  circular  path.  It  is  evident  that  when  its  degree 


182  ELEMENTS   OF  SCIENCE 

of  eccentricity  (i.e.,  its  greatest  departure  from  a  circular 
path)  is  greatest,  the  pole  which  when  thus  most  distant 
from  the  sun,  is  also  inclined  away  from  it,  must  then 
endure  a  very  exceptional  degree  of  cold.  Of  course,  at 
such  a  time,  the  opposite  pole  and  hemisphere  must  be 
very  exceptionally  warm. 

The  direction  also  of  the  earth's  axis  slightly  varies, 
each  pole  describing  a  circle  (comparable  with  that 
described  by  the  summit  of  a  revolving  teetotum)  in  a 
very  long  period  of  time;  that  is  to  say,  in  nearly 
twenty-six  thousand  years.  This  movement  is  spoken  of 
as  the  precession  of  the  equinoxes,  because  each  change  in 
the  position  of  the  earth's  axis  necessarily  changes  the 
position,  in  the  earth's  orbit,  of  the  spot  where  equal  day 
and  night  are  experienced  all  over  the  globe. 

Evidently  from  the  great  proximity  of  the  moon  to 
the  earth,  there  must  be  an  energetic  action  of  gravity 
between  them,  and  this  energy  must  produce  its  most 
conspicuous  effect  upon  what  is  at  once  most  easily 
moved  and  can  most  plainly  be  seen  to  be  so  moved. 

That  which  is  thus  most  easily  and  evidently  moved,  is 
the  earth's  liquid  investment — the  ocean.  The  effect  of 
the  action  of  gravity  between  the  earth  and  the  moon,  is 
made  manifest  by  the  tides — the  moon  raising  up  the 
surface  of  the  sea  as  it  revolves  round  the  earth.  This 
action  is,  of  course,  modified  by  that  of  the  sun,  but  on 
account  of  the  enormous  distance  of  the  latter,  its  action 
is  much  less  than  that  of  our  satellite.  Did  the  moon 
act  alone,  and  were  the  earth  perfectly  spherical  and 
everywhere  covered  with  a  uniform  depth  of  water,  the 
moon  would  so  attract  the  water  that  there  would  be 
one  great  wave,  or  heap  of  water,  directly  beneath  it, 
and  another  on  the  opposite  side  of  the  globe,  the  water 
in  the  interspace  being  correspondingly  depressed. 


THE   NON-LIVING  WORLD  183 

Thus  it  is  (i)  when  the  sun  and  moon  are  exactly  opposite 
each  other,  the  world  being  between  them  (which  is 
the  time  of  full  moon),  and  (2)  when  they  are  on  the  same 
side,  or  in  conjunction,  the  world  being  opposite  both 
(which  is  the  time  of  new  moon),  that  their  combined 
actions  produce  the  very  high  tides.  The  intermediate 
periods  give  rise  to  the  relatively  slight,  or  "neap," 
tides. 

The  ellipticity  of  the  earth's  orbit  and  also  that  of 
the  moon,  cause  variations  in  the  proximity  of  these 
bodies  to  each  other  and  to  the  sun.  It  is  when  the  sun 
and  moon  are  thus  nearest  to  us,  that  we  get  the  very 
high  or  "  spring  "  tides. 

The  various  configurations  of  tracts  of  land  and  water, 
and  their  geographical  positions,  variously  modify  the 
times  and  degrees  of  elevation  in  the  tides  of  different 
places.  Thus,  for  example,  the  Mediterranean  is  an 
almost  tideless  sea. 

An  action,  which  is  so  visible  with  respect  to  the 
ocean,  must  also  take  place  in  the  atmosphere,  and  thus, 
as  before  mentioned,*  there  must  be  atmospheric  tides, 
though  they  do  not  make  their  existence  conspicuous. 

The  phenomena  known  as  "falling  stars"  are  due  to 
the  attraction  to  the  earth  of  minute  cosmical  bodies, 
meteorites,  which  it  encounters  in  its  path  round  the 
suu.  These  bodies  afford  us  the  plainest  proof  that  the 
same  chemical  substances  exist  in  the  solar  system, 
external  to  this  earth,  as  exist  in  the  earth  itself.  But 
the  careful  study  of  the  spectrum — spectrum  analysis — 
which  can  be  obtained  from  the  light  of  the  stars,  tends 
to  show  us  that  a  similar  identity  of  materials  exists 
between  the  substances  which  compose  our  own  planet  and 

*  See  ante,  p.  153. 


184  ELEMENTS   OF   SCIENCE 

those  which  enter  into  the  composition  of  even  the 
most  distinct  stellar  bodies.  Thus  the  action  of  gravity 
and  the  energies  known  as  light,  heat,  motion  and 
chemical  action,  as  also,  doubtless,  those  activities  termed 
electric  and  magnetic,  seem  to  be  diffused  throughout 
the  visible  universe.  The  same  is  doubtless  the  case 
with  other  energies  and  influences,  if  such  there  be, 
which  remain,  as  yet,  undiscovered  and  unknown. 

These  few  elementary  notions  with  respect  to  the 
heavenly  bodies,-  and  the  effects  of  their  energies  upon 
the  globe  we  inhabit,  are  all  which  space  permits  us 
to  give.  For  more  than  an  introduction  to  such  first 
elements  of  science,  the  student  must  be  referred  to  works 
devoted  to  the  exposition  of  the  science  of  astronomy. 


CHAPTER  VI 
THE  LIVING  WORLD 

WE  have  now,  in  our  study  of  elementary  science, 
to  make  a  great  step  in  advance.  The  objects 
which  have  next  to  occupy  our  attention,  like  those 
which  have  previously  occupied  it,  conform,  as  a  matter 
of  course,  to  the  laws  of  number  and  of  mechanics,  and 
serve  as  vehicles  for  the  physical  forces  herein  before 
noticed.  But  the  objects  we  have  now  to  consider  also 
possess  additional  powers — powers  of  which  the  whole 
non-living  world  is  entirely  destitute.  Every  one  knows 
that  plants  grow  and  multiply,  and  that  animals  not 
only  grow  and  multiply,  but  have  their  feelings  also. 
Our  dog  can  plainly  hear  and  see  us,  and  has  his  sensa- 
tion of  pleasure  and  of  pain,  as  well  as  his  emotions  of 
hope  and  joy,  of  fear  and  grief,  But  so  highly  organ- 
ised an  animal  cannot  serve  to  set  forth  the  subject  of 
this  chapter.  For  by  "  the  living  world,"  the  whole  mass 
of  creatures,  from  the  humblest  green  thread  of  conferva, 
or  most  microscopic  fungus,  to  the  gigantic  gum-tree 
and  the  far-spreading  banyan  ;  and  from  the  hardly  per- 
ceptible animalcule  to  the  humming-bird,  the  condor,  the 
tiger,  the  whale,  the  monkey  and  man. 

To  study  so  enormous  a  mass  of  forms  with  any  com- 
pleteness is  beyond  the  power  of  any  single  human 
being. 

It  is  therefore  absolutely  impossible  in  this  chapter  to 


1 86  ELEMENTS   OF   SCIENCE 

do  more  than  indicate  what  the  various  branches  of  such 
a  study  are,  and  to  briefly  portray  some  of  the  most 
elementary  and  indisputable  facts  which  concern  living 
beings.  For  everything  beyond  this,  students  are  re- 
ferred to  the  many  special  treatises  which  exist  on  each 
of  the  numerous  sub-divisions  of  the  study  of  living 
creatures  considered  as  one  whole. 

The  study  of  that  living  whole — the  science  which 
includes  the  study  of  all  living  things — is  termed  biology, 
while  botany  treats  only  of  plants,  and  zoology  exclusively 
of  animals. 

.  The  living  creatures  with  which  we  are  familiar,  have 
various  active  powers,  while  every  animal  or  plant  has  a 
certain  structure  of  its  own.  The  most  casual  observa- 
tion suffices  to  show  that  a  fowl,  a  lobster  and  an  oyster, 
a  rose-tree,  a  Scotch  fir,  a  mushroom  and  a  sea-weed, 
have  each  of  them  a  structure  more  or  less  different  from 
that  of  each  of  the  others.  There  is  a  science  which 
deals  with  obvious  structural  differences,  namely  ana- 
tomy. That  word,  taken  by  itself,  generally  refers  to  the 
study  of  the  structure  of  the  human  body,  while  the 
structure  of  other  animals,  compared  therewith,  is 
spoken  of  as  comparative  anatomy.  But  plants  have  also 
their  anatomy,  though  their  structures  are  much  simpler 
than  that  of  most  animals. 

The  material  frame  of  an  animal  or  plant  may  soon 
be  seen  to  consist  of  different  kinds  of  substances.  Thus 
a  cat's  body*  will  be  found  to  consist  of  fur,  skin,  flesh, 
nerves,  bones,  &c.  Similarly,  a  tree,  such  as  an  elder, 
will  be  seen  to  be  made  up  of  woody  substance,  solid  and 


*  Readers  are  referred  to  the  author's  work  on  the  cat  (John 
Murray)  as  a  complete  introduction  to  all  branches  of  the  study 
of  living  things. 


THE   LIVING  WORLD  187 

hollow  fibres,  pith,  leaf-substance,  &c.  Now  these 
various  substances  are  called  tissues,  and  each,  when 
examined  by  the  microscope,  is  found  to  be  composed  of 
very  small  structures,  which  are  for  the  most  part  known 
as  "  cells."  The  study  of  tissues  and  their  minute 
structure  is  called  histology. 

Anatomy  shows  us  that  living  creatures  are  composed 
of  various  parts  of  organs,  each  made  up  of  certain 
tissues.  Thus  the  cat,  like  man,  is  provided  with  a 
mouth  to  receive  food,  teeth  to  divide  and  crush  it,  a 
stomach  to  digest  it,  an  alimentary  canal  and  liver,  a 
heart  and  blood-vessels,  a  brain  and  nerves,  &c.,  each 
being  composed  of  the  various  tissues  which  enter  into 
its  composition.  An  oak  also  has  its  stem,  containing 
many  tubular  vessels,  roots  which  spread  into  the  soil, 
and  leaves  which  expand  and  expose  themselves  to  the 
sun's  rays.  All  these  different  parts  or  organs  concur  in 
sustaining  the  life  of  the  creature  which  possesses  them, 
and  therefore  the  life  of  its  various  other  organs. 

In  this  way  each  organ  is  reciprocally  "end"  and 
"means";  on  which  account  living  creatures  are  com- 
monly spoken  of  as  organisms.  Organs  are  also  united 
together  into  groups  which  are  called  il  systems"  Thus 
the  mouth,  stomach,  intestine,  liver,  &c.,  constitute  what 
is  called  the  alimentary  system;  the  heart  and  vessels 
form  the  vascular  or  circulating  system,  and  the  brain 
and  nerves  the  nervous  system. 

Now  all  these  various  component  parts  of  living  crea- 
tures have  their  respective  activities  or  functions,  which 
minister  to,  and  are  subsumed  in,  the  life  of  the  creature 
itself.  The  study  of  these  various  functions  or  activities 
is  termed  physiology. 

Each."  cell "  has  its  own  activity,  as  has  each  "  tissue " 
(formed  of  cells  of  one  kind)  and  each  "  organ  "  (formed  of 


i88  ELEMENTS   OF   SCIENCE 

different  tissues)  and  each  "system"  (consisting  of  various 
organs),  the  harmony  of  all  the  "  systems  "  resulting  in 
the  life  of  the  creature  whereof  such  "  systems  "  are  com- 
ponent parts. 

Certain  lowly  organisms  consist  but  of  a  single  cell, 
and  are  therefore  spoken  of  as  unicellular. 

We  know  that  an  animal  (e.g.,  the  cat)  eats,  digests, 
and  so  nourishes  itself,  circulates  its  blood,  breathes, 
forms  (i.e.,  secretes)  saliva,  bile,  &c. ;  feels,  moves  to  and 
fro,  and  may  become  the  parent  of  another  generation. 
These  various  life  activities,  or  functions,  are  respectively 
known  as  alimentation,  nutrition,  circulation,  respiration, 
secretion,  sensation,  locomotion,  and  generation.  Every 
one  knows  also  that  plants  and  animals  grow,  as  also 
that  plants  generally  spring  from  seeds,  and  birds  from 
eggs. 

The  study  of  that  particular  growth  which  takes 
place  in  a  plant  from  the  seed,  and  in  the  bird  from 
the  formation  of  the  egg,  is  called  embryology. 

But  animals  and  plants  have  very  definite  relations 
with  space  and  time.  Monkeys  and  armadillos  do  not 
exist  in  a  wild  state  in  England,  and  kangaroos  are 
found  nowhere,  naturally,  save  in  the  Australian  region ; 
nor  are  cacti,  which  are  so  common  in  Mexico,  found 
wild  in  Scotland.  There  is,  then,  a  science  of  the 
geography  of  organisms.  They  have  also  definite 
relations  to  past  time.  A  multitude  of  animals  and 
plants  which  existed  in  Eocene*  times  do  not  live  now, 
and  this  is  still  more  the  case  with  the  reptiles  whose 
remains  are  found  fossil  in  the  secondary  strata,  while  it 
is  clear  that  many  animals  which  now  live  did  not  do 
so  in  those  earlier  periods.  Thus,  organisms  have 

*  See  ante,  p.  169, 


THE   LIVING   WORLD  189 

definite  relations  with  past  time  as  well  as  with  space  ; 
and  it  is  evident  that  a»s  age  has  succeeded  age,  there 
has  been  a  process  of  replacement  in  vegetable  and 
animal  forms,  new  kinds  having  come  into  being  one 
after  another.  It  seems  also  evident  that  in  the  earliest 
ages  the  world  was  entirely  devoid  of  living  creatures. 

Furthermore,  animals  and  plants  have  also  definite  rela- 
tions with  each  other.  If  a  beast  of  prey  finds  its  way 
into  a  region  peopled  with  creatures  good  for  food,  it 
will  increase  and  multiply  to  their  detriment ;  while  the 
most  peaceful  animal  will  suffer,  by  the  introduction, 
into  a  limited  area,  of  creatures  which  are  rivals  because 
they  feed  upon  the  same  food,  the  supply  of  which  will, 
sooner  or  later,  be  insufficient  for  all.  Here  the  reader 
may  ask,  if  the  world  was  once  without  life,  whence  did 
life  come  ? — and  what  is  life  ?  Also,  since  new  kinds 
have  replaced  older  ones  which  disappeared,  the  question 
naturally  arises,  how  did  new  kinds  arise  ? 

But  in  a  work  like  the  present  one  (which  is  but  an 
introduction  to  the  elements  of  science),  the  con- 
sideration of  such  questions  would  be  out  of  place. 
They  would  be  as  much  out  of  place  a,s  would  be  a 
consideration  of  the  questions  "What  is  heat?"  and 
"  What  is  light  ?  "  As  to  the  latter  questions  we  have 
provisionally  noted  certain  useful  working  hypotheses. 
Similarly,  since  up  to  the  present  day,  life  has  not  been 
evolved  by  us  from  inorganic  matter,  we  may,  as  a  work- 
ing hypothesis,  adopt  the  belief  that  life  is  the  energy 
of  a  peculiar  form  of  force  which  exists  differently  in 
each  different  kind  of  organism,  and  that  this  force  is  a 
main  agent  in  the  development  of  new  kinds.  As  to 
the  first  introduction  of  life  on  the  surface  of  this  planet 
our  reason  is  as  yet  entirely  in  the  dark. 

Tho   number   of    all   the    various   kinds    of    living 


190  ELEMENTS   OF   SCIENCE 

creatures  is  so  enormous  that  it  would  be  impossible  to 
study  them  profitably,  were  they  not  classified  in  an 
orderly  manner.  Therefore  the  whole  mass  has  been 
divided,  in  the  first  place,  into  two  supreme  groups, 
fancifully  termed  kingdoms — the  "  animal  kingdom" 
and  the  "  vegetal  kingdom."  Each  of  these  is  sub- 
divided into  an  orderly  series  of  subordinate  groups, 
successively  contained  one  within  the  other,  and  named 
sub-kingdoms,  classes,  orders,  families,  genera  and  species. 
The  lowest  group  but  one  is  the  "  genus,"  which 
contains  one  or  more  different  kinds  termed  "  species," 
as  e.g.,  the  species  "wood  anemone"  and  the  species 
"  blue  titmouse."  The  lowest  group  of  all — a  species — 
may  be  said  to  consist  of  individuals  which  differ  from 
each  other  only  by  trifling  characters,  such  as  characters 
due  to  difference  of  sex,  while  their  peculiar  organisation 
is  faithfully  reproduced  by  generation  as  a  whole,  though 
small  individual  differences  exist  in  all  cases. 

The  vegetal,  or  vegetable,  kingdom,  consists  of  the 
great  mass  of  flowering  plants,  many  of  which,  however, 
have  such  inconspicuous  flowers  that  they  are  mis- 
takenly regarded  as  flowerless,  as  is  often  the  case  with 
the  grasses,  the  pines,  and  the  yews.  Another  mass, 
or  sub-kingdom,  of  plants  consists  of  the  really  flower- 
less  plants,  such  as  the  ferns,  horsetails  (Fig.  26),  lyco- 
pods,  and  mosses.  Sea  and  fresh-water  weeds  (algce),  and 
mushrooms,  or  "  moulds,"  of  all  kinds  (fungi),  amongst 
which  are  the  now  famous  "  bacteria"  constitute  a 
third  and  lowest  set  of  plants. 

The  animal  kingdom  consists,  first,  of  a  sub-kingdom 
of  animals  which  possess  a  spinal  column,  or  backbone, 
and  which  are  known  as  vertebrate  animals.  Such  are 
all  beasts,  birds,  reptiles,  and  fishes.  There  are  also  a 
variety  of  remotely  allied  marine  organisms  known  as 


THE   LIVING   WORLD  191 

tunicates,  sea-squirts,  or  ascidians  (Fig.  27).  There  is, 
further,  an  immense  group  of  arthropods,  consisting  of 
all  insects,  crab-like  creatures,  hundred-legs  and  their 
allies,  with  spiders,  scorpions,  tics  and  mites.  We 

FIG.  26. 


HORSE-TAIL  (Equisetum  drummondii). 

have  also  the  sub- kingdom  of  shell-fish  or  molluscs, 
including  cuttle-fishes,  snails,  whelks,  limpets,  the 
oyster,  and  a  multitude  of  allied  forms.  A  multi- 
tudinous sub-kingdom  of  worms  also  exists,  as  well  as 


192 


ELEMENTS   OF   SCIENCE 


FIG.  27. 


another  of  star-fishes  and  their  congeners.  There  is  yet 
another  of  zoophytes,  or  polyps,  and  another  of  sponges, 
and,  finally,  we  have  a  sub-kingdom  of  minute  creatures, 
or  animalculce,  of  very  varied  forms,  which  may  make  up 
the  sub-kingdom  of  Protozoa,  consisting  of  animals  which 
are  mostly  unicellular. 

Multitudinous  and  varied  as  are  the  creatures  which 
compose  this  immense  organic  world, 
they  nevertheless  exhibit  a  very  re- 
markable uniformity  of  composition 
in  their  essential  structure.  Every 
living  creature,  from  a  man  to  a  mush- 
room, or  even  to  the  smallest  animal- 
cule or  unicellular  plant,  is  always 
partly  fluid,  but  never  entirely  so. 
Every  living  creature  also  consists 
in  part  (and  that  part  is  the  most 
actively  living  part)  of  a  soft,  vis- 
cid, transparent,  colourless  substance, 
termed  protoplasm,  which  can  be 
resolved  into  the  four  elements,*  oxy- 
gen, hydrogen,  nitrogen  and  carbon. 
Besides  these  four  elements,  living 
organisms  commonly  contain  sulphur, 
phosphorus,  chlorine,  potassium,  so- 
dium, calcium,  magnesium  and  iron. 
In  the  fact  that  living  creatures  always  consist  of 
the  four  elements,  oxygen,  hydrogen,  nitrogen  and 
carbon,  we  have  a  fundamental  character,  whereby  the 
organic  and  inorganic  (or  non-living)  worlds  are  to  be 
distinguished.  For,  as  we  have  seen,  inorganic  bodies, 
instead  of  being  thus  uniformly  constituted,  may  consist 


A   TUNICATE 

(Ascidia). 


*  See  ante,  pp.  138-140. 


THE   LIVING  WORLD  193 

of  the  most  diverse  elements  and  sometimes  of  but  two  or 
even  of  only  one. 

Again,  many  minerals,  such  as  crystals,*  are  bounded 
by  plain  surfaces  and,  with  very  few  exceptions,f  none  are 
bounded  by  curved  lines  and  surfaces,  while  living 
organisms  are  bounded  by  such  lines  and  surfaces. 

Yet  again,  if  a  crystal  be  cut  through,  its  internal 
structure  will  be  seen  to  be  similar  throughout.  But  if 
the  body  of  any  living  creature  be  divided,  it  will,  at  the 
very  least,  be  seen  to  consist  of  a  variety  of  minute 
distinct  particles,  called  "granules,"  variously  distributed 
throughout  its  interior. 

All  organisms  consist  either  (as  do  the  simplest,  mostly 
microscopic,  plants  and  animals)  of  a  single  minute  mass 
of  protoplasm,  or  of  a  few,  or  of  many,  or  of  an  enormous 
aggregation  of  such  before-mentioned  particles,  each  of 
which  is  one  of  those  bodies  named  a  "cell"  (Fig.  28, 
p.  1 95).  Cells  may,  or  may  not,  be  enclosed  in  an  investing 
coat  or  "  cell-wall."  Each  cell  generally  contains  within  it 
a  denser,  normally  spheroidal,  body  known  as  the  nucleus. 

Now  protoplasm  is  a  very  unstable  substance  (as  we 
have  seen  many  substances  are  whereof  nitrogen  J 
is  a  component  part),  and  it  possesses  active  properties 
which  are  not  present  in  the  non-living,  or  inorganic 
world.  In  the  latter,  differences  of  temperature  will 
produce  motion  in  the  shape  of  "  currents,"  as  we  have 
seen  §  with  respect  to  masses  of  air  and  water.  But  in  a 
portion  of  protoplasm,  an  internal  circulation  of  currents 
in  definite  lines  will  establish  itself  from  other  causes. 

Inorganic  bodies,  as  we  have  seen,  will  expand  with 

*  See  ante,  p.  143. 

t  Spathic  and  hematite  iron  and  dolomite  are  such  exceptions. 
%  See  ante>  p.  139.  §  See  ante  pp.  150-157. 

N 


194  ELEMENTS   OF   SCIENCE 

heat,  as  they  may  also  do  from  imbibing  moisture ;  but 
living  protoplasm  has  an  apparently  spontaneous  power 
of  contraction  and  expansion  under  certain  external 
conditions  which  do  not  occasion  such  movements  in 
inorganic  matter. 

Under  favouring  conditions,  protoplasm  has  a  power 
of  performing  chemical  changes,  which  result  in  producing 
heat  far  more  gently  and  continuously  than  it  is  produced 
by  the  combustion  of  inorganic  bodies.  Thus  it  is  that 
the  heat  is  produced  which  makes  its  presence  evident  to 
us  in  what  we  call  "  warm-blooded  animals,"  the  most 
warm-blooded  of  all  being  birds. 

Protoplasm  has  also  the  wonderful  power  of  trans- 
forming certain  adjacent  substances  into  material  like 
itself — into  its  own  substance — and  so,  in  a  sense, 
creating  a  new  material.  Thus  it  is  that  organisms  have 
the  power  to  nourish  themselves  and  grow.  An  animal 
would  vainly  swallow  the  most  nourishing  food  if  the 
ultimate,  protoplasmic  particles  of  its  body  had  not  this 
power  of  "transforming"  suitable  substances  brought 
near  them  in  ways  to  be  hereinafter  noticed. 

Without  that,  no  organism  could  ever  "  grow."  The 
growth  of  organisms  is  utterly  different  from  the  increase 
in  size  of  inorganic  bodies.  Crystals,  as  we  have  seen,* 
grow  merely  by  external  increment ;  but  organisms  grow 
by  an  increment  which  takes  place  in  the  very  innermost 
substance  of  the  tissues  which  compose  their  bodies  and 
the  innermost  substance  of  the  cells  which  compose 
such  tissues;  this  peculiar  form  of  growth  is  termed 
intussusception. 

Protoplasm,  after  thus  augmenting  its  mass,  has  a 
further  power  of  spontaneous  division,  whereby  the  mass 

*  See  ante,  pp.  143  and  144. 


THE  LIVING  WORLD  195 

of  the  entire  organism  whereof  such  protoplasm  forms  a 
part,  is  augmented  and  so  growth  is  brought  about. 

The  small  particles  of  protoplasm  which  constitute 
"  cells  "  are  far  indeed  from  being  structureless.  Besides 
the  nucleus  already  mentioned  there  is  a  delicate  net- 
work of  threads  of  a  substance  called  chromatin  within 
it,  and  another  network  permeating  the  fluid  of  the  cell 
substance  which  invests  the  nucleus,  often  with  further 
FIG.  28. 


C 

CELL   FROM   A   SALAMANDER. 

«,  nucleus;  n',  nucleolus  embedded  in  the  network  of  chromatiu 
threads ;  k,  network  of  the  cell  external  to  the  nucleus ;  a, 
attraction-sphere  or  archoplasra  containing  minute  bodies  called 
centrosomes ;  cl,  membrane  enclosing  the  cell  externally ;  n/, 
membrane  surrounding  the  nucleus  ;  c,  centrosomes. 

[Drawn  by  Mr.].  E.  S.  Moore.'] 

complications.  These  networks  generally  perform  (or 
undergo)  a  most  complex  series  of  changes  every  time  a 
cell  spontaneously  divides.  In  certain  cases,  however, 
it  appears  that  the  nucleus  divides  into  two  in  a  more 
simple  fashion,  the  rest  of  the  cell  contents  subsequently 
dividing — each  half  enclosing  one  part  of  the  previously 
divided  nucleus.  It  is  by  a  continued  process  of  cell 
division  that  the  complex  structures  of  the  most  com- 
plex organisms  is  brought  about. 


196  ELEMENTS    OF   SCIENCE 

The  division  of  a  cell,  or  particle  of  protoplasm,  is 
indeed  a  necessary  consequence  of  its  complete  nutrition. 

For  new  material  can  only  be  absorbed  by  its  surface. 
But  as  the  cell  grows,  the  proportion  borne  by  its  surface 
to  its  mass,  continually  decreases ;  therefore  this  surface 
must  soon  be  too  small  to  take  in  nourishment  enough  ? 
and  the  particle,  or  cell,  must  therefore  either  die  or 
divide.  By  dividing,  its  parts  can  continue  the  nutritive 
process  till  their  surface,  in  turn,  becomes  insufficient, 
when  they  must  divide  again  and  so  on.  Thus  the  term 
" feeding"  has  two  senses.  " To  feed  a  horse,"  ordinarily 
means  to  give  it  a  certain  quantity  of  hay,  oats  or  what 
not ;  and  such  indeed  is  truly  one  kind  of  feeding.  But 
obviously,  if  the  nourishment  so  taken  could  not  get  from 
the  stomach  and  intestine  into  the  ultimate  particles 
and  cells  of  the  horse's  body,  the  horse  could  not  be 
nourished  and  still  less  could  it  grow.  It  is  this  latter 
process,  called  assimilation,  which  is  the  real  and  essential 
process  of  feeding,  to  which  the  process  ordinarily  so 
called  is  but  introductory. 

Protoplasm  has  also  the  power  of  forming  and  ejecting 
from  its  own  substance,  other  substances  which  it  has 
made  but  which  are  of  a  different  nature  to  its  own. 
This  function,  as  before  said,  is  termed  secretion  ;  and  we 
know  the  liver  secretes  bile  and  that  the  cow's  udder 
secretes  milk. 

Here  again  we  have  an  external  and  an  internal 
process.  The  milk  is  drawn  forth  from  a  receptacle,  the 
udder,  into  which  it  finds  its  way,  and  so,  in  a  superficial 
sense,  it  may  be  called  an  organ  of  secretion.  Neverthe- 
less the  true  internal  secretion  takes  place  in  the  inner- 
most substance  of  the  cells  or  particles  of  protoplasm,  of 
the  milk-gland,  which  particles  really  form  that  liquid. 

But  every  living  creature  consists  at  first  entirely  of 


THE   LIVING   WORLD  197 

a  particle  of  protoplasm.  Therefore  every  other  kind  of 
substance  which  may  be  found  in  every  kind  of  plant  or 
animal,  must  have  been  formed  through  it,  and  be,  in 
fact,  a  secretion  from  protoplasm.  Such  is  the  rosy 
cheek  of  an  apple,  or  of  a  maiden,  the  luscious  juice  of 
the  peach,  the  produce  of  the  castor-oil  plant,  the  baleen 
that  lines  the  whale's  enormous  jaws,  as  well  as  that 
softest  product,  the  fur  of  the  chinchilla.  Indeed  every 
particle  of  protaplasm  requires,  in  order  that  it  may  live, 
a  continuous  process  of  exchange.  It  needs  to  be  con- 
tinuously first  built  up  by  food,  and  then  broken  down 
by  discharging  what  is  no  longer  needful  for  its  healthy 
existence.  Thus  the  life  of  every  organism  is  a  life  of 
almost  incessant  change,  not  only  in  its  being  as  a  whole, 
bat  in  that  of  all  its  protoplasmic  particles  also. 

Prominent  among  such  processes  is  that  of  an  inter- 
change of  gases  between  the  living  being  and  its  environ- 
ment. This  process  consists  in  an  absorption  of  oxygen 
and  a  giving- out  of  carbonic  acid,  which  exchange  is 
termed  respiration. 

Lastly,  protoplasm  has  a  power  of  motion  when 
appropriately  acted  on.  It  will  then  contract  or  expand 
its  shape  by  alternate  protrusions  and  retractions  of 
parts  of  its  substance.  These  movements  are  termed 
amoebiform,  because  they  quite  resemble  the  movements 
of  a  small  animalcule  which  is  named  amoeba  (Fig.  29). 

Such  is  the  ultimate  structure,  and  such  are  the 
fundamental  activities  (or  functions)  of  living  organisms 
(so  far  as  they  can  here  be  described),  from  the  lowest 
animalcule  and  unicellular  plant,  up  to  the  most  complex 
organisms  and  the  body  of  man  himself. 

It. has  been  explained  how  it  is  that  organisms  of 
complex  structure  become  such  by  means  of  a  spon- 
taneous division  and  multiplication  of  their  component 


I98 


ELEMENTS   OF  SCIENCE 


cells.  Many  unicellular  organisms  also  divide  them- 
selves into  two  equal  halves,  which  each  grow  as  large 
as  was  the  previously  undivided  cell.  Thus  new 
individuals  are  generated  in  the  simplest  fashion 
imaginable. 

Other  forms  send  forth  more  or  less  delicate  pro- 
longations of  their  substance,  at  the  ends  of  which 
minute  cells,  termed  spores,  are  produced,  each  of  which, 
under  favourable  circumstances,  will  grow  up  into  the 
form  of  the  parent  which  produced  it. 

Minute   water-weeds,  which   may   consist  of    but  a 

FIG.  29. 


AMCEBA    SHOWN    IN    TWO   OF   THE    MANY    IRREGULAR 

SHAPES  IT  ASSUMES.     (After  Howes,} 

The  clear  space  within  it  is  a  contractite  vesicle.  The  dark  body  is 
the  nucleus.  In  the  right-hand  figure  there  is  shown  a  particle 
of  food,  passing  through  the  external  surface. 

thread-like  single  series  of  cells  (confervce)  will,  when 
two  such  threads  are  adjacent,  produce  spores  by  con- 
jugation. For  this  purpose,  processes  from  opposite  cells 
of  two  such  thread-like  plants,  will  grow  forth,  meet, 
and  then  blend  together  their  protoplasmic  contents. 
The  result  of  this  process  is  the  production  of  a  spore, 
which  will  afterwards  grow  into  another  conferva — 
thread.  Those  multicellular  fungi  known  as  ."pun- 
balls,"  give  forth,  when  ripe,  such  a  multitude  of 
minute  "spores"  as  to  resemble  a  puff  of  smoke — 


THE   LIVING   WORLD 


199 


whence  their  name.  That  part  of  a  mushroom,  which 
rises  from  the  ground,  is  also  a  "  spore  "  producer. 

The  cells  of  plants  are  enclosed  in  a  cell-wall  which 
consists  of  a  substance  known  as  cellulose,  and  which 
contains  no  nitrogen. 

The  unicellular  water- weeds  (algce)  contain  a  green 
substance  termed  chlorophyll,  which  somehow  enables 
them,  during  daylight,  to  dissolve  carbonic  acid  and 
retain  its  carbon,  while  they  let  its  oxygen  go  free. 

FIG.  30. 


PORTIONS   OF   FIVE   THREADS    OF   Conferva, 
GREATLY    MAGNIFIED. 

Showing  the  cells  of  which  they  are  composed  and  also  the  protrusion 
and  blending  of  prominences  of  some  of  the  cells,  and  the  passage 
of  the  protoplasmic  cell-contents  through  two  of  the  protrusions 
which  have  blended. 

Such  plants  can,  in  this  way,  nourish  themselves  and 
live  on  inorganic  substances.  Fungi,  on  the  other  hand, 
which  possess  no  chlorophyll,  and  are  not  green,  cannot 
do  this,  and  therefore  require  for  food  living  matter,  or 
matter  which  has  lived.  Both  kinds  of  plants  respire, 
and  therefore  both,  in  breathing,  take  oxygen  from  the 
air  and  give  out  into  it  carbonic  acid  from  their  own 
substance  in  exchange,  but  it  is  only  the  green  plants 


200  ELEMENTS   OF  SCIENCE 

which  give  out  oxygen,  when  feeding,  by  absorbing  the 
carbon  of  the  atmospheric  carbonic  acid. 

All  the  higher  plants  resemble,  in  this  respect,  the 
green  unicellular  ones,  and  therefore  enormous  volumes 
of  oxygen  are  given  forth  by  the  vast  forests  and  exten- 
sive grassy  plains  which  clothe  the  earth's  surface,  as 
also  by  the  masses  of  seaweed  in  the  ocean. 

There  is  a  sea-weed  called  Lessonia  which  forms  sub- 
marine forests,  with  stems  like  the  trunks  of  ordinary 
trees,  while  the  sea-weed  called  Macrocystis  may  attain  a 
length  of  700  feet.  The  group  of  small  sea-plants 
known  as  Floridice  are  amongst  the  most  delicate  and 
elegant  of  vegetable  structures. 

pJG  ..,.  Animals,  like  fungi,  cannot  dissolve  car- 

bonic acid,  absorb  its  carbon  and  let  its 
oxygen  go  free;  but  in  breathing  they  all 
give  forth  large  quantities  of  carbonic  acid, 
at  the  same  time  absorbing  a  great  amount 
PROTOCOCCUS  °f  t^ie  oxygen  given  forth  by  green  plants. 

with  two      This  is  the  reason  why  animals  soon  become 

Vibmtile      suffocated  when  enclosed  in  anything  which 

Cilia.  denies  them  a  supply  of  fresh  air.  When  so 
enclosed,  they  soon  exhaust  the  supply  of  oxygen  avail- 
able, and  die  of  suffocation,  because  they  can  then  no 
longer  exchange  their  carbonic  acid  for  it. 

Some  of  the  lower  plants  move  about  in  water  with 
much  activity,  as  for  example,  does  the  alga  called  Proto- 
coccus  (Fig.  31),  which  moves  by  means  of  two  minute  hair- 
like  processes  termed  vibratile  cilia,  which  effect  repeated 
lashings,  the  cause  of  which  is,  as  yet,  quite  unexplained. 
Another  very  simple  plant  is  called  Volvox  (Fig.  32),  and 
consists  of  a  spheroidal  aggregation  of  cells  bearing 
outwardly  a  multitude  of  projecting  cilia,  the  regular 
lashings  of  which  cause  the  spheroidal  whole  to  rotate, 


THE   LIVING   WORLD 


201 


FIG.  32. 


while  young  spheroidal  aggregations  are  formed  within 
the  parent. 

Some  plants,  as  the  well-known  sensitive  plant,  move 
their  leaflets  on  being  touched.  Others  will  move  parts 
of  their  flowers,  either  for  the  purpose  of  setting  seed,  or 
for  protection,  or  for  some  other  reason  (as  the  pimpernel 
will  close  its  flowers  under  a  clouded  sky),  or  to  project 
their  seeds  to  a  considerable  distance,  as  is  the  case 
with  certain  balsams.  There  are  two  kinds  of  plant, 
however,  which  are  quite 
exceptional  in  the  move- 
ments they  will  effect.  The 
first  of  these  is  the  sun- 
dew of  the  genus  Drosera. 
The  upper  surfaces  of  its 
leaves  bear  certain  hair-like 
processes  which  can  dis- 
charge a  tenacious  fluid. 
Any  insect,  settling  upon 
the  leaf,  is  apt  to  be  caught 
by  these  processes,  which 
bend  over  it  and  bathe  it  Volvox  globator,  MUCH  MAGNIFIED. 
in  the  fluid  they  distil.  Showing  ribratile  cilia  on  its  sur- 
The  other  plant  is  called  face  and  numerous  young  con- 
TT  ,  a  /TT  \  tained  within  it. 

venus s  ny-trap  (-big.   33) 

(Dioncea).  Its  leaves  terminate  in  two  rounded  expan- 
sions, joined  by  a  median  hinge,  and  they  bear  strong 
bristles  along  their  margins.  When  an  insect  alights  on 
this  structure,  the  two  rounded  expansions  snap  sharply 
together  and  imprison  it. 

Such  phenomena  are,  indeed,  different  from  any  to  be 
met  with  in  the  non-living  world,  though  they  are,  of 
course,  nothing  to  the  complex  movements  of  animals. 
Everybody  knows  that,  as  a  rule,  plants  hardly  move  at 


202 


ELEMENTS   OF   SCIENCE 


FIG.  33. 


all,  while  active  locomotion  is  the  common  characteristic 

of  the  animal  kingdom. 

It  is  absolutely  impossible  in  this  work  to  give  even 

the  merest  outline  of  all 
the  principal  groups  of 
plants  and  animals.  For 
further  information  the 
reader  is  referred  to  works 
devoted  to  botany  and  zoo- 
logy. We  must  content 
ourselves  with  selecting  a 
flowerless  and  a  flowering 
plant  as  examples  of  vege- 
table life,  adding  thereto 
a  brief  notice  of  a  few 
leading  types  from  the 
animal  kingdom. 

Passing  by,  therefore, 
the  lichens,  liverworts, 
mosses,  lycopods,  and 
horsetails,  and  leaving 
the  student  to  seek  a 
knowledge  of  them  else- 
where, we  will  briefly  con- 
sider the  common  bracken 
fern,  called  by  botanists 
Pteris  aquilina  —  Pteris 
being  the  name  of  the 
genus  to  which  it  belongs, 

and    aquilina    indicating 
Showing  flower  above  and  the  fly-  whi(jh  species  ft  js  of  that 
catching  leaves  round  its  base. 

genus. 

It  is  an  organism  of  considerable  size  made  up  of  a 
multitude  of  cells  variously  transformed  to  constitute 


VENUS'S  FLY-TRAP  (Dionaa 
muscipula). 


THE   LIVING  WORLD 


203 


the  different   "tissues"    whereof   the    entire   plant   is 
made  up. 

The  fern  consists  of  an  axial  portion  corresponding  to 

the  stem  of  most  plants,  which  runs  along  underground, 

giving  off  at  intervals  the  parts  which  appear  above 

ground  and  are  called  fronds.     These  fronds  correspond 

FIG.  34. 


BRACKEN-FERN  (Pteris  aqidlino). 

Showing  fronds  springing  from  underground  stem,  which  gives 
out  rootlets  beneath. 

with  the  leaves  of  ordinary  plants ;  and  all  leaves,  however 
modified,  are  distinguished,  by  the  term  foliar  organs, 
from  stems,  which,  however  modified,  are  called  axial 
organs.  Roots,  in  the  form  of  filamentary  processes, 
are  given  off  from  the  under  surface  of  the  creeping 
subterranean  stem  or  rhizome.  The  latter  is  formed 


204  ELEMENTS   OF   SCIENCE 

of  differently  shaped  cells  aggregated  in  masses  so  as  to 
appear  as  bands  of  different  colours  when  it  is  cut 
transversely.  These  bands  consist  of  fibres  and  tubes 
amidst  large  polygonal  cells  containing  many  granules 
of  starch — which  is  a  non-nitrogenous  substance  that 
plants  produce  abundantly. 

The  fronds  are  green,  flattened  and  much  sub-divided 
expansions,  invested  on  their  upper  surface  with  a  layer 
of  irregularly  shaped  cells  forming  what  is  called  the 
epidermis.  Beneath  this  is  a  mass  of  cells  containing 
chlorophyll,  which  gives  its  green  colour  to  the  frond. 
The  under  surface  of  the  frond  is  coated  with  cells  and 
hair-like  processes,  while  between  many  of  the  cells 
are  small  openings,  termed  stomata,  which  allow  air  to 
enter  and  penetrate  the  cavities  (left  between  the  cells 
which  form  the  substance  of  the  frond),  termed  inter  - 


Thus  the  important  process  of  dissolving  carbonic  acid 
and  fixing  its  carbon  while  its  oxygen  is  set  free,  takes 
place  in  the  interior  of  the  plant,  as  well  as  does  the 
process  of  respiration. 

If  a  frond  be  cut  during  summer,  another  will  soon 
grow  up,  and  takes  its  place.  Thus  we  have  a  process 
of  reparative  growth,  much  more  complex  and  complete 
than  is  the  reparation  of  a  mutilated  crystal,  or  plant- 
like  aggregations  of  crystals,  which  is  the  nearest 
approximation  to  true  "  growth "  that  is  to  be  met 
with  in  the  non-living  world.  In  the  fern,  however,  we 
have  a  mode  of  growth  to  which  nothing  in  the  non-living 
world  makes  even  the  faintest  approximation. 

Under  the  margin  of  a  full-grown  frond  will  be  found 
a  groove  containing  a  series  of  small  brown  bodies,  each 
of  which  is  called  a  sporangium,  because  it  is  a  little 
membranous  bag  that  contains  spores,  which  bag  bursts 


THE   LIVING   WORLD 


205 


and  scatters  the  spores  when  ripe.     Each  such  spore  is  a 

double-walled  cell  containing  protoplasm.     If  it  falls  on 

a  suitable  surface  it  gives  forth  a  prolongation,  the  cells 

FIG.  35. 


an 


PROTHALLUS    AND    ITS  PARTS    MAGNIFIED. 


A  Whole  prothallus. 

s     Spore. 

r     Boot  filaments  or  rhizoids. 

an  Antheridia. 

ar  Archegonia. 

B  An  archegonium  greatly  mag- 
nified. 

cc.  Canal  cells. 


ce.c.  Central  cells. 
C  Two   antheridia  greatly   mag- 
nified. 
an  Antherozoids  escaping  from 

one  of  them. 

D  Antherozoids  still   more  mag- 
nified. 


formed  from  which  divide  and  subdivide  till  they  form  a 
small  cake-like  expansion  termed  a  protliallus,  which 
sends  down  root-fibres  from  its  under  surface. 

Then  there  appear  on  the  prothallus  a  few  rounded 


206  ELEMENTS  OF  SCIENCE 

prominences,  each  of  which  is  called  an  antheridium,  and 
contains  within  it  cells,  from  each  of  which  there  comes 
forth  a  little  spiral  body  bearing  many  cilia,  by  means  of 
which  it  can  move  actively  about.  This  little  corkscrew- 
like  structure  is  termed  an  antherozoid.  Meantime  on 
the  prothallus  other  prominences  have  appeared,  each  of 
which  is  called  an  archegonium,  and  is  a  small  cellular 
tube  (th'e  walls  of  which  are  formed  by  "canal  cells"), 
open  at  its  apex,  and  exposing  to  view  a  central  cell 
at  the  bottom  of  the  tube.  This  distinct  cell  is 
denominated  an  oosphere,  or  embryo  cell,  and  remains 
quiescent  till  one  of  the  antherozoids  finds  its  way  to  it 
and  blends  with  it.  It  is  a  process  which  may  remind 
us  of  the  process  of  conjugation  between  different  cells 
of  confervas  and  is  termed  impregnation.  When  it  has 
taken  place,  the  embryo  cell  divides  and  subdivides  till 
it  forms  an  incipient  rhizome  with  its  rootlet  and  this 
young  stem  soon  throws  up  a  frond,  and  so  the  original 
form  of  the  fern  is  reproduced. 

Thus  we  have  not  only  growth  and  change,  but  a  cycle 
of  changes,  and  what  is  sometimes  spoken  of  as  "an 
alternation  of  generations."  Thus  we  have  : 

(1)  A  fern-organism,  which  produces 

(2)  A  prothallus-organism,  from  which 

(3)  A  fern-organism  again  results.     As    before  said, 
nothing   even   faintly  approximating   to   this   cycle   of 
changes,  occurs  anywhere  amongst  bodies  devoid  of  life. 

Let  us  next  examine  the  structure  and  life-processes 
of  a  bean  plant  (Vicia  faba).  Here  we  have  an  axial 
organ,  or  stem,  which  is  not  a  rhizome  but  grows 
upwards  from  the  soil,  giving  forth  roots  from  its  base. 
From  opposite  sides  of  the  stem  spring  forth  foliar 
organs,  in  the  form  of  green  leaves,  and  also  branches,  or 
ramifications  of  the  axis,  which  again  bear  green  foliage 


THE   LIVING  WORLD 
FIG.  36. 


207 


PLANT  (Vicid  faba). 

A  With  root,  rootlets,  stem,  foliage  leaves, 
and  flowers. 

B  A  flower  vertically  bisected  to  show 
the  ovules  within  the  pistil,  beyond 
the  free-end  of  which  the  stamens 
bend  upwards,  each  terminating  in  a 
pollen-bearing  anther.  External  to 
the  stamens  two  of  the  petals  are  to 
be  seen,  external  to  the  base  of  whic^i 
are  two  sepals  of  the  calyx. 


208  ELEMENTS   OF   SCIENCE 

leaves  on  either  side.  These  foliar  leaves  are  essentially 
like  the  frond  in  structure  and  function  save  that  they 
bear  no  spores. 

But  there  are  other  foliar  organs  which  grow  forth 
around  delicate  ramifications  of  the  axis,  and  which  form 
what  we  know  as  "  the  flower."  The  green  foliar  organs 
are  separated  from  each  other  by  interspaces  consisting 
of  successive  portions  of  the  axis ;  but  these  interspaces 
are  suppressed  in  the  flower,  so  that  its  foliar  organs  are 
all  closely  approximated.  First  comes  a  ring  of  green 
foliar  organs  which  are  evidently  but  slightly  modified 
leaves.  There  are  five  of  them,  each  of  which  is  called  a 
sepal,  while  the  whole  five  constitute  what  botanists 
name  the  calyx.  Then  comes  a  ring  of  five  more  modified 
and  differently  coloured  leaves,  each  of  which  is  called  a 
petal,  the  whole  five  petals  forming  what  is  known  as  the 
corolla.  Within  the  corolla  are  ten  filamentary  bodies 
(stamens),  each  ending  in  an  oval  expansion,  or  anther, 
which  contains  a  fine  yellow  powder  termed  pollen.  Each 
particle  of  this  powder  is  called  a  pollen-grain.  Lastly, 
in  the  centre  of  the  flower  is  a  single  body  known  as  the 
pistil,  whereof  the  upper  portion  is  termed  the  style,  at 
the  extremity  of  which  is  a  somewhat  modified  surface, 
spoken  of  as  the  stigma.  The  pistil  is  hollow  and,  if  cut 
open,  will  be  found  to  contain  small  bodies  named  ovules, 
which  are  attached  to  its  inner  surface  by  short  stalks. 

The  ovule  is  very  far  from  being  a  simple  cell,  like  the 
oosphere  of  a  'fern.  In  the  first  place  it  is  enclosed 
in  two  coats,  except  at  one  point,  called  the  micropyle, 
while  amongst  the  cells,  of  which  the  small  body  consists, 
is  one  of  larger  size,  termed  the  embryo  sac,  within  which 
again  two  thickenings  arise,  from  the  upper  one  of 
which  the  future  plant  develops  itself  subsequent  to  im- 
pregnation, while  the  lower  one  affords  it  nourishment. 


THE   LIVING   WORLD 


209 


The  agent  of  impregnation  is  a  pollen  grain,  every  one  of 
which  consists  of  a  fluid  particle  of  protoplasm,  enclosed 
in  a  membrane  or  wall,  which  is  almost  always  double. 

As  the  yellow  pollen  dust  flies  about,  one  grain  sooner 
or  later  is  wafted  to  the  stigma  of   the  pistil,  or,  as 
in    very   many   plants,    is 
carried    there    by    insects 
in    search    of    food,    who 
have      previously      dusted 
themselves  with  pollen  in 
visiting  other  plants.     As 
soon    as    the    pollen-grain 
finds  itself  there,  the  par- 
ticle of  protoplasm,  enclosed 
in    its    inner   coat,   passes 
through  its  outer  one  and 
descends  through  the  inter- 
cellular spaces  of  the  style 
till   it    reaches    an   ovule.          DIAGRAM  OF  AN  OVULE. 
Then  it  passes  through  the  Vertically  bieected  and  showing  th 
micropyle,  or  minute  aper-         two  coats  which  enclose  it. 
ture  left  in  the  ovule's  two  E  Embryo  sac. 


coats,   and    penetrates   its  M  M'cr<wlf  °/.  ™™**   opening 

through  which  the  pollen-  tube 
substance  till  it  reaches  the 


embryo   sac    which  it  im- 

mu       4.v 
pregnates.   Then  the  upper 

thickening  within  it  (before 


enters. 
Upper  thickening  of  cell-con- 

tents,    in    which  the   embryo 
of  ^  ^^  plant  ^  ^ 

origin. 

spoken  of)  grows  and  de-  T2  Lower  thickening. 
velops,  from  a  mere  formless  mass  of  cells,  into  a  miniature 
plant  with  a  minute  rudimentary  stem  and  root  and  two 
pairs  of  leaves.  Two  of  these  leaves  are  termed  the 
cotyledons.  They  become  of  relatively  enormous  size, 
enclosing  the  minute  plant  between  them  and  constitut- 
ing the  great  mass  of  the  seed  we  familiarly  know  as  "  a 

o 


210  ELEMENTS   OF  SCIENCE 

bean."  Meanwhile  the  pistil,  which  encloses  the  growing 
ovules,  itself  rapidly  enlarges  into  a  pod,  which,  when 
ripe,  bursts  and  sets  free  the  ovules  which  have  now 
become  seeds,  after  which  it  decays. 

When  the  seed,  the  bean,  finds  its  way  to  the  earth, 
under  fixed  conditions  of  warmth  and  moisture,  it 
germinates.  This  process  of  germination  consists  in  the 
bursting  of  the  seed-coat  by  the  swelling  cotyledons, 
which  become  green  and  emerge  as  fleshy  leaves,  while 
the  miniature  stem  ascends  and  the  little  root  descends, 
both  meantime  absorbing  nutriment  from  the  cotyle- 
dons. 

The  stem  of  the  adult  bean  plant  is  of  complex 
structure,  its  component  cells  having  become  modified 
into  different  tissues. 

As  to  the  physiology  of  the  bean  plant,  it  may  be 
divided  into  (i)  the  functions  which  minister  to  the 
preservation  of  the  individual  and  (2)  those  which 
concern  the  preservation  of  the  race. 

Liquid  is  absorbed  by  the  roots  and  part  of  it  evapo- 
rates, by  what  is  called  transpiration,  from  the  surfaces 
of  the  leaves,  whence  air  and  vapour  are  conveyed 
inwards — through  their  stomata.*  Thus  a  sort  of 
circulation  also  takes  place.  Liquid  ascends  between 
the  fibres  of  the  stein,  being  drawn  up  through 
evaporation  from  the  leaves  and  being  pushed  up 
by  the  absorption  of  the  roots.  Water  with  suitable 
salts  t  in  solution  (nitrates  of  potassium  or  of  calcium  and 
sulphates  of  iron  or  of  magnesium)  is  absorbed  by  the 
roots,  while  carbon  is  fixed  by  the  decomposition  of 
carbonic  acid,  during  daylight,  by  the  green  leaves. 
These  processes  result  in  the  formation  of  cellulose, 


*  See  ante,  p.  204.  t  See  ante,  p.  134. 


THE   LIVING   WORLD  211 

starch,  sugar  and  other  products.  The  ascending  fluids 
permeate  from  cell  to  cell  upwards,  while  the  products 
of  carbon-fixation  permeate  from  cell  to  cell  inwards. 
Slow  oxidation,  or  oxygenation  (respiration),  meantime 
takes  place  in  the  ultimate  component  cells  of  the  plant, 
the  respired  air  (containing  much  carbonic  acid)  mean- 
while diffusing  itself  and  escaping.  During  daylight  the 
balance  of  discharge  is  largely  in  favour  of  the  oxygen, 
but  at  night  the  balance  of  discharge  is  in  favour  of  the 
carbonic  acid. 

Thus  the  plant  lives  and  grows  by  the  exercise  of  the 

FIG.  38. 


A   LEAF   OF   BRYOPHYLLUM. 

Showing  two  young  plants  springing  from  its  margin. 
(After  Geddes.) 

functions  of  absorption,  circulation,  feeding  (or  alimen- 
tation) by  its  cells,  together  with  respiration  and  se- 
cretion. 

Generation,  by  the  aid  of  the  two  sexual  products  (i) 
the  pollen  tube,  and  (2)  the  embryo  cell,  provides  for  the 
preservation  of  the  race;  but  this  is  also  abundantly 
provided  for  in  plants  by  another  process — by  a  sexless 
(asexual)  process  of  generation.  In  many  plants  aggre- 
gations of  cells  form  buds,  called  bulbils,  which  become 
detached  and  then  grow  into  a  new  individual  plant. 


212  ELEMENTS   OF  SCIENCE 

Such  are  the  bulbils  which  form  themselves  at  the  roots 
of  the  leaves  of  the  tiger-lily.  Some  ferns  give  rise  to 
fresh  individuals  from  the  surface  of  their  fronds,  and 
a  plant  named  Bryophyllum  calycinum  (Fig.  38)  forms 
buds  at  the  margin  of  its  leaves,  from  which  buds  new 
individuals  grow  forth.  Every  one  knows  how  common 
it  is  for  fresh  individual  plants,  new  trees,  to  grow  from 
"cuttings,"  and  the  constancy  with  which  plants  will 
repair  injuries  and  reproduce  lost  parts  after  pruning, 
FIG.  39. 


VERTICAL  SECTION  OF  A  BUTTERCUP. 

Showing  the  floral  organs  which  spring  successively  from  its  axis. 
At  the  bottom  are  two  of  the  sepals  (of  the  calyx)  cut  through. 
Next  come  three  of  the  five  petals  (of  the  corolla).  Then  come 
numerous  stamens  (each  terminating  in  its  anther),  which  sur- 
round six  bisected  carpels  (of  the  pistil),  each  showing  an 
ovule  contained  within  it. 

is  so  notorious  that  the  only  surprise  the  reader  may 
probably  feel  in  perusing  this  statement  will  be  surprise 
that  so  well  known  a  fact  should  be  referred  to  at  all. 

Every  kind  of  flower  and  fruit  can  be  understood 
through  the  flower  of  the  bean  plant,  however  different 
from  it  they  may  appear  to  be.  Flowers,  such  as  those 
of  the  daisy,  the  dandelion  and  the  thistle,  are  aggrega- 
tions of  flowers  set  closely  side  by  side  upon  a  common 
surface;  each  separable  little  group  of  minute  parts  in 


THE   LIVING  WORLD  213 

such  flowers  being  a  perfect  or  more  or  less  imperfect 
flower  in  itself,  on  which  account  such  plants  are  termed 
composite. 

In  such  a  flower  as  the  buttercup  there  is  no  single 
body  for  a  pistil,  as  in  the  bean,  but  instead  of  it  there 
is  a  number  of  independent  separate  parts,  each  of 
which  is  called  a  carpel,  and  has  its  stigma  on  its  summit, 
so  that  we  might  say  there  is  a  number  of  pistils,  were 
it  not  against  the  custom  of  botanists  so  to  express  the 
fact.  Very  often  various  parts  are  suppressed,  and 
sometimes  a  flower  may  consist  merely  of  a  single 
stamen  or  a  single  pistil.  Such  flowers  are,  of  course, 
of  one  sex  only,  and  when  a  plant  has  such  flowers 
but  bears  both  kinds — as  does  the  cucumber — it  is 
said  to  be  monoecious.  In  some  plants,  however,  as 
in  the  willow,  each  tree  is  of  one  sex,  and  bears  only 
male  or  only  female  flowers.  Such  a  plant  is  termed 
dicecious. 

For  all  further  information  about  plants  the  reader  is 
referred  to  treatises  on  botany,  as  our  remaining  space 
must  be  devoted  to  a  brief  notice  of  the  structures  and 
functions  found  amongst  animals. 

With  respect  to  unicellular  animals,  little  need  be 
said,  because  their  structures  and  functions  so  little 
exceed  those  of  the  lowest  plants.  It  must  suffice  to  say 
that  there  is  a  large  group  called  Rhizopods,  because  they 
can  protrude  and  detract  either  long  or  short,  thick  or 
filamentary  processes  of  their  protoplasmic  body-sub- 
stance. The  most  beautiful  of  these  are  the  marine 
Radiolaria,  the  bodies  of  which  often  contain  the  most 
wonderfully  symmetrical  and  complex  silicious  skeletons. 
There  are  also  the  Foraminifera,  so  called  because  their 
processes  pass  out  through  minute  holes  in  the  calcareous 
shells  they  form  around  their  most  simple  bodies.  We 


2I4 


ELEMENTS   OF  SCIENCE 


have  already  of  spoken  the  Amoeba,*  which  protrudes 
short  blunt  processes,  and  so  changes  its  shape  in  the 
most  protean  fashion.  All  these  creatures  feed  by  simply 
taking  in  their  food  at  any  point  of  the  surface  of  their 
bodies  and  similarly  discharging  what  they  cannot 
digest.  There  are  also  the  Flagellata,  which  swim  about 
FIG.  40. 


A   RADIOLARIAN  (AuloSCCHa  miYObills]  GREATLY    MAGNIFIED. 

by  the  aid  of  one  or  more  vibratile  cilia,  as  does  the 
plant  Protococcus  before  described. t  Then  comes  the 
great  group  of  Infusoria,  which  are  slightly  more 
complex  in  structure  and  bear  bands  of  vibratile  cilia. 

Sponges    come   next,  which,    very   simply   organised 
multicellular  organisms,  have   their   cells   arranged    in 


*  See  ante,  pp.  197  and  198. 


t  See  ante,  p.  200. 


THE   LIVING   WORLD 


215 


AN    INFUSORIAN  (Vorticella)  GREATLY    MAGNIFIED. 

One  individual  has  its  stem  contracted,  while  that  of   the  other  is 
stretched  out. 

y    Contractile  fibre  in  the   stalk 

not  contracted. 
Cilia. 

Upper  surface  or  disc. 
Fibre  in  a  contracted  state. 


C.I 

d 

a 

nc  Nucleus. 


p  One  end  of  the  region  surround- 
ing the  month. 

rf  Space  surrounding  a  particle  of 
food. 

re  Contractile  vesicle  or  space. 

vs  Vestibule  or  chamber  extend- 
ing inwards  from  the  mouth. 
(After  Howes. 


216 


ELEMENTS   OF   SCIENCE 


two  layers,  and  contain  silicious,  calcareous,  or  horny 
skeletons.  They  have  also  a  number  of  inhalent  and 
exhalent  apertures. 

The   zoophytes,  or  plant-like  animals  (which  include 

FIG.  42. 


Hydra  viridis. 

So-called  foot.  .  t1  Tentacles  not  fully  grown. 

h  Mouth.  *  Prey  seized. 

t    One  of  the  tentacles. 

(After  Howes.) 

the  coral-forming  polyps,  which  live  aggregated  toge- 
ther), the  jelly  fishes,  sea  anemones,  &c.,  succeed  the 
sponges.  The  simplest  form  of  the  group  is  the  Hydra, 
which  consists  of  a  sack  with  a  single  aperture  sur- 


THE   LIVING   WORLD  217 

rounded  by  tentacles,  the  whole  body  being  made  up  of 
two  layers  of  cells,  which  nevertheless  give  signs  of 
forming  most  simple  muscle-substance  and  nerve-sub- 
stance, tissues  to  be  more  distinctly  referred  to  shortly. 
Another  great  group  consists  of  the  star-fishes,  sea- 
urchins,  crinoids,  &c.,  all  of  which  are  called  Echino- 
derms,  and  though  essentially  simple  in  structure,  may 
consist  of  a  prodigious  number  of  small  juxtaposed 
calcareous  parts. 

Next  may  be  mentioned  the  small  animals  known  as 
wheel-animalcules,  and  minute  creatures  which  live  in 
compound  aggregation,  such  as  the  well-known  sea-mat 
Flustra  (often  popularly  regarded  as  a  seaweed),  which 
minute  creatures  are  termed  Bryozoa  or  Polyzoa. 

A  multitude  of  creatures  are  known  as  worms.  Such 
are  the  many  internal  parasites,  with  their  allies,  and 
also  leeches,  earthworms,  and  aquatic  worms. 

To  these  succeed  the  two  great  groups  of  (i)  arthropods 
and  (2)  molluscs.*  Of  their  structure,  however,  we  will 
say  nothing  till  we  have  first  briefly  described  the 
organisation  and  functions  of  one  of  the  highest  class 
of  backboned  animals — that  to  which  we  belong — which 
class  comprises  all  mammals  (or  mammalia),  so  called 
because  their  females  give  suck  to  their  young  through 
their  mammary  glands  and  breasts. 

From  this  class,  which  includes  all  beasts,  we  will 
select  the  cat  for  consideration,  as  that  will  well  serve  to 
show  how  great  is  the  difference  between  the  most  complex 
inorganic  body  and  a  highly  organised  living  creature. 

The  external  form  of  the  cat  needs  no  description 
here.  Beneath  its  skin  lies  the  flesh,  and  these  enclose 
the  bones — skull,  backbone,  ribs,  and  limb-bones. 


*  See  post,  pp.  234-238. 


2i8  ELEMENTS   OF   SCIENCE 

Within  the  trunk  is  a  cavity  containing  the  heart, 
lungs,  kidneys,  stomach,  intestine,  liver,  &c.  Within 
the  skull  and  backbone  is  a  mass  of  white  substance — the 
brain  and  spinal  marrow.  Delicate  threads  of  this  white 
substance  (nerves), and  also  tubes  of  various  sizes  (vessels), 
traverse  the  body  in  all  directions.  The  various  "  organs  " 
are,  as  before  said,  grouped  in  "i systems,"*  and  are 
composed  of  "tissues."  Thus,  "fat"  is  adipose  tissue, 
flesh  is  muscular  tissue,  the  outermost  layer  of  the  skin 
is  epithelial  tissue,  and  its  deeper  layer  is  formed  of 
connective  tissue.  Bone  is  osseous  tissue,  the  brain  and 
nerves  are  nervous  tissue,  gristle  is  cartilaginous  tissue? 
and  the  blood  may  be  termed  sanguineous  tissue. 

The  body  is  reducible  to  the  ultimate  chemical 
elements  above  enumerated, t  but  before  this  extreme 
reduction  to  its  ultimate  elements  it  can  be  shown  to 
consist  of  certain  complex  organic  compounds  or  proxi- 
mate  elements,  such  as  albumen  (the  substance  of  the 
white  of  egg)  and  gelatine  (the  substance  of  jelly),  and 
others. 

The  flesh  consists  of  a  multitude  of  delicate  threads 
called  "  muscular  fibres,"  which  are  variously  aggregated 
in  masses,  and  so  form  muscles.  The  heart  is  a  four- 
chambered  muscular  organ,  the  centre  of  two  sets  of  tubes 
— arteries  and  veins — the  extremities  of  which  are  con- 
nected by  minute  vessels  termed  capillaries. 

A  third  set  of  vessels — lymphatics — converge  from  all 
parts  of  the  body  to  two  large  veins.  The  arteries, 
veins  and  heart,  are  full  of  blood,  and  the  lymphatics  of 
an  almost  colourless  fluid  called  lymph.  These  fluids 
contain  a  multitude  of  minute  bodies  termed  "  blood 
corpuscles."  which  are  of  two  kinds,  white  and  red. 

*  See  ante,  p.  187.  f  See  ante,  p.  192. 


THE   LIVING  WORLD  219 

The  lungs  are  two  very  complexly  formed  air-bags, 
while  a  tube — the  windpipe — descends  from  the  back  of 
the  mouth,  bifurcates  below  and  then  ramifies  in  each 
lung,  the  whole  constituting  the  "  respiratory  system." 
The  membrane  which  lines  certain  parts  of  this  system 
is  coated  with  cilia  * — like  those  of  infusoria,  or  those  by 
which  the  protococcus  effects  its  movements. 

Each  kidney  is  a  rounded  mass  of  minute  tubes,  which 
converge  to  open  into  a  cavity  whence  a  tube  descends 
to  the  bladder  which  opens  externally  by  a  further 
canal. 

The  skeleton  is  made  up  of  bones  and  cartilages,  and 
the  parts  are  mostly  capable  of  being  moved  one  upon 
another  by  the  intervention  of  the  muscles  which  are 
attached  to  them.  These  movements  are  facilitated  by 
the  shape  of  the  contiguous  surfaces  of  such  movable 
bones,  which  constitute  what  are  called  articulations  or 
"joints." 

The  essential  part  of  the  generative  system  of  the 
male,  consists  of  very  minute  tubes  which  form  small 
bodies  analogous  to  the  antherozoids  of  ferns.  They 
are  rounded  bodies  which  move  by  the  aid  of  a  single 
cilium  only,  and  are  called  spermatozoa. 

The  essential  generative  organs  of  the  female  do  not 
consist  of  tubes,  but  of  a  peculiar  solid  substance  con- 
taining modified  cells  termed  ova. 

The  nervous  system  consists  of  an  immense  multitude 
of  cords,  threads,  and  cells  containing  a  peculiar  albu- 
minous fluid,  These  form  the  brain,  spinal  cord,  nerves, 
and  small  rounded  aggregations  of  nervous  substance 
termed  ganglia.  Nerves  proceed  from  the  nervous  axis 
(brain  and  spinal  cord)  to  all  parts  of  the  body,  and 

*  See  ante,  p.  200. 


220  ELEMENTS   OF   SCIENCE 

certain  special  nerves  pass  from  the  brain  to  the  eye,  the 
ear  and  nose,  and  the  tongue. 

That  to  the  eye  expands  into  a  delicate  membrane  of 
nervous  tissue  (of  wonderfully  complex  construction) 
called  the  retina,  upon  which  an  image  of  external  things 
is  projected  according  to  the  laws  of  light,*  as  in  a 
camera  obscura,  owing  to  the  various  different  trans- 


H 

VERTICAL    SECTION    OF    A   LION'S    EYE. 


Aq  Aqueous  humour. 

Ch  Choroid  coat. 

Cm  Ciliary  muscle. 

On  Cornea. 

Cp  Ciliary  processes. 

Cr  Crystalline  lens. 


Ir    Iris. 

Op  Optic  nerve. 

R    Muscle  of  the  eyeball. 

Rt   Eetina. 

Scl  Sclerotic  coat. 


parent  media  placed  in  front  of  the  retina  and  forming 
the  bulk  of  the  eye -ball. 

The  true  organ  of  hearing,  or  internal  ear,  is  a  com- 
plexly-shaped, membranous  bag  (containing,  and  floating 
in,  fluid)  on  which  the  auditory  nerve  ramifies. 

The  organ  of  smell  consists  of  minute  branches  of 
nerves  which  proceed  from  two  forward  prolongations  of 

*  See  ante,  p.  107. 


THE   LIVING   WORLD  221 

the  brain,  and  ramify  in  the  membrane  which  lines  the 
back  of  the  nostrils.  Similarly  the  tongue  and  hinder 
part  of  the  palate  are  supplied  with  tasting  or  gustatory 
nerves  which  also  proceed  from  the  brain,  though  from 
quite  its  hinder  portion . 

The  spinal  cord  gives  off  nerves  on  either  side 
symmetrically  in  pairs,  each  nerve  arising  by  two 
roots,  one  from  the  front  and  one  from  the  back  of 
the  cord.* 

The  cat's  body  possesses  what  is  called  bilateral  sym- 
metry, that  is  to  say  there  is  a  close  resemblance  and 
correspondence  between  its  right  and  left  sides,  though 
this  does  not  apply  to  all  its  internal  organs.  There  is 
also  a  serial  symmetry  as,  e.g.,  between  the  front  and 
the  hind  leg,  between  the  successive  ribs  of  either 
side,  and  between  the  successive  bones  which  together 
make  up  the  back-bone. 

Such  being  the  structure  of  the  cat,  we  have  next  to 
consider  its  physiology — the  functions  of  its  various  parts. 

We  have  seen  that  protoplasm  has  a  power  of  con- 
traction. This  exists  greatly  intensified  in  muscular 
tissue,  and  all  the  cat's  movements  are  performed 
through  contractions  of  its  muscles  which  move  the 
bones  to  which  they  are  attached,  causing  them  to  act 
like  levers  of  different  orders.f  Thus,  when  the  cat 
raises  its  fore-paw  to  strike,  the  paw  is  the  weight,  the 
fulcrum  is  the  lower  end  of  the  bone  of  the  upper  part 
of  the  fore-leg,  and  the  force  or  motive  power  is  the 
muscle  which  is  attached  to  a  bone  of  the  lower  part  of 
the  fore-leg,  and  which,  by  its  contraction,  raises  the 
paw,  and  so  this  action  is  an  example  of  a  lever  of  the 
third  order. 

*  See  Fig.  44,  p.  226.  f  See  ante,  p.  51. 


222  ELEMENTS   OF   SCIENCE 

Protoplasmic  mobility  is  seen  in  the  white  corpuscles 
of  the  blood,  which  can  change  their  shape  as  does  an 
amoeba,  which  indeed  they  closely  resemble. 

It  is  also  shown  by  the  action  of  the  cilia  of  the 
respiratory  system,  which  move  harmoniously  .like  the 
stalks  of  a  field  of  corn  under  a  strong  wind.  The 
result  of  this  is  that  they  propel  forwards  any  small 
body  which  may  be  upon  them,  and  thus  the  breathing 
organs  become  liberated  from  various  matters  which  are 
so  borne  upwards  towards  the  mouth. 

The  great  process  of  nourishing  the  body  is  effected 
through  the  mechanical  division  of  food  by  the  cat's  teeth 
and  its  solution  by  the  juices  of  the  spittle-glands,  the 
stomach,  and  the  alimentary  canal,  into  which  canal  the 
secretions  of  the  liver  and  pancreas  are  poured.  These 
juices  so  act  on  the  food  as  to  change  many  of  its  com- 
ponent parts  from  an  insoluble  into  an  easily  soluble 
state  —  namely*  from  "colloids"  into  "crystalloids," 
but,  as  before  said,  the  final  process  consists  of  what  is 
called  assimilation,  or  the  transformation  of  matter  ex- 
ternal to  the  most  intimate  substance  of  the  cat's  body, 
into  that  very  substance — the  change  of  the  food  it  eats 
into  the  cat  itself. 

But  besides  nutriment,  the  animal  requires  that  its 
body  should  be  kept  at  a  certain  temperature,  and  this 
is  effected  by  that  continuous  process  of  slow  combus- 
tion f — oxygenation — before  mentioned. 

But  nutrition  could  not  be  effected  were  not  fresh 
nutritive  material  conveyed  all  over  the  body  to  replace 
wear  and  tear ;  and  it  is  so  conveyed  by  the  circulating 
system,  the  blood  exuding  from  the  finest  capillary  vessels, 
to  reach  the  ultimate  cells  and  structures  of  the  body. 

*  See  ante,  p.  145.  f  See  ante,  p.  194. 


THE   LIVING   WORLD  223 

But  the  blood  after  being  thus  impoverished,  itself 
requires  replenishment,  and  this  it  obtains  from  the 
nutritive  material  gathered  from  the  alimentary  canal 
by  the  lymphatics,  and  subsequently  poured  into  the 
blood. 

Of  all  the  functions  of  the  body,  that  of  respiration 
is  the  most  conspicuously  necessary  for  the  maintenance 
of  life,  since  the  separate  life  of  the  cat  begins  with  an 
act  of  inspiration,  while  it  is  with  an  act  of  expiration 
that  it  ceases.  A  short  interruption  of  the  process 
necessarily  results  in  death.  In  breathing,  the  air  is 
taken  down  into  the  lungs,  and  is  thence  again  expelled 
much  poorer  in  oxygen  but  containing  a  much  increased 
quantity  of  carbonic  acid,  because  the  blood  which  conies 
to  the  lungs  from  all  parts  of  the  cat's  frame  liberates 
into  them  the  excess  of  carbonic  acid  it  has  obtained 
from  the  ultimate  substance  of  the  body  and,  in  ex- 
change, takes  from  the  air  in  the  lungs,  the  oxygen 
requisite  to  supply  that  ultimate  substance  with  the 
oxygen  it  needs. 

Thus,  in  such  an  animal  as  the  cat,  there  is  both  an 
internal  and  an  external  process  of  respiration.  The 
former  consists  of  the  gaseous  exchange  which  takes 
place  in  the  ultimate  particles  of  the  body.  The  latter 
is  the  gaseous  exchange  which  takes  place  in  the  lungs 
themselves. 

Closely  connected  with  respiration  and  nutrition  is 
the  process  named  secretion,  which  is  the  special  func- 
tion of  such  organs  as  are  called  glands.  Two  most  im- 
portant organs  of  the  cat's  body  are  the  kidneys,  which 
secrete  and  remove  from  the  blood  certain  effete  and 
deleterious  nitrogenous  substances.  The  salivary  glands, 
liver  and  pancreas,  pour  their  respective  secretions  (spittle, 
bile,  and  pancreatic  juice)  into  the  alimentary  canal,  the 


224  ELEMENTS   OF   SCIENCE 

walls  of  which  are  replete  with  small  glands,  as  are  those 
of  the  stomach,  which  latter  secrete  gastric  juice. 

The  generative  function  is  a  special  modification  and 
form  of  "  growth,"  while  growth  is  a  sort  of  self-genera- 
tion. This  is  specially  perceptible  when  any  part  which 
has  been  destroyed  is  reformed,  as  when  a  broken  bone 
is  repaired.  Then  the  two  broken  edges  become 
softened,  and  a  substance  is  secreted  between  them 
which  is  at  first  jelly-like,  then  gristle-like,  and  at  last 
bony.  In  generation,  impregnation  is  effected  by  the 
junction  of  the  spermatozoon  with  the  ovum,  which  is  a 
process  essentially  similar  to  that  of  the  union  of  anthe- 
rozoid  and  pollen  tube,  with  the  female  cells  of  the  fern 
and  of  the  bean  plant.  Immediately  after  impregnation 
very  curious  changes  ensue,  which  cannot  here  be  de- 
scribed, the  reader  being  referred  for  their  explanation  to 
treatises  on  embryology.*  Here  it  must  suffice  to  say 
that  the  first  germ  of  the  future  animal  appears  in  the 
shape  of  a  minute  rounded  mass  of  protoplasm,  which 
divides  and  divides  itself  again  and  again  till  three  layers 
of  cells  are  formed,  whence,  by  degrees,  all  the  varied 
tissues  and  all  the  complex  parts  which  constitute 
the  kitten  are  gradually  but  rapidly  built  up.  The 
building  up  of  the  kitten,  as  it  exists  at  birth,  goes  on 
nevertheless  in  a  roundabout  fashion,  various  structures 
being  for  a  time  formed  which  resemble  conditions  that 
are  permanent  in  lower  animals^  but  which  subsequently 
disappear  or  become  much  modified. 

The  functions  of  the  cat's  nervous  system  merit  some 
special  consideration,  since  without  its  aid  none  of  its 
other  bodily  activities  could  be  carried  on.  Its  functions 
also  present  the  most  extreme  contrast  yet  met  with  to 

*  And  to  my  work  on  the  cat,  p.  317. 


THE   LIVING  WORLD  2^5 

each  and  all  of  the  powers  possessed  by  inorganic  bodies. 
The  processes  of  growth  and  generation  are  different 
indeed  from  the  activities  of  non-living  bodies,  but  far 
more  divergent  is  the  power  of  feeling,  of  perceiving  by 
the  senses  surrounding  objects,  and  of  regulating  bodily 
actions  in  conformity  thereto.  Sensitivity  is  the  special 
attribute  of  nervous  tissue,  and  each  creature's  nervous 
system  is  thus  an  organ  of  intervention  between  it  and 
the  world  around  it. 

Sensation  can  be  absolutely  known  only  to  the  being 
that  experiences  it;  nevertheless  it  would  be  in  the 
highest  degree  absurd  not  to  be  certain  that  a  cat  feels, 
sees,  hears,  smells,  and  tastes,  and  that  it  possesses  feelings 
of  pleasure  and  pain,  with  propensions,  desires,  and 
emotions  of  affection,  fear,  animosity,  &c.  But  different 
parts  of  the  nervous  system  have  different  functions,  as 
is  the  case  with  different  parts  of  one  portion  of  it. 
Thus  part  of  the  spinal  cord  transmits  an  influence  up- 
wards to  the  brain,  resulting  in  sensation,  while  another 
part  transmits  an  influence  downwards  from  the  brain, 
resulting  in  movement.  The  ascending  sensitive  in- 
fluence passes  to  the  cord  through  the  posterior  roots  of 
the  spinal  nerves  into  which  enter  the  nervous  fibres 
terminating  in  the  skin,  and  which  are  affected  when  the 
skin  is  touched.  The  descending  motive  influence  passes 
from  the  cord  through  the  anterior  roots  of  the  spinal 
nerves,  which  ramify  and  terminate  in  the  muscles  where 
they  produce  motion. 

It  is  not,  however,  necessary  that  such  influence 
should  actually  ascend  to,  or  descend  from,  the  brain  in 
order  that  responsive  motions  should  take  place,  although 
it  is  certain  (from  observations  made  on  accidentally 
injured  men  and  purposely  mutilated  animals)  that  the 
brain  must  act  in  order  to  give  rise  to  sensation. 

p 


•226 


ELEMENTS   OF  SCIENCE 


When  the  influence  originated  by  touching,  pricking, 
or  burning  some  part — e.g.,  some  part  of  the  leg — is  pre- 
vented by  any  cause  from  reaching  the  brain,  while 
none  the  less  some  appropriate  action  follows — e.g.,  the 
withdrawal  of  a  foot  from  a  hot  iron,  without  the  occur- 
rence of  any  sensation — such  response  is  called  reflex 
action.  The  unfelt  influence  travelling  upwards  and 
inwards  is  supposed,  on  reaching  the  spinal  cord  through 
the  posterior  roots  of  its  nerves,  to  be  there  auto- 
matically reflected  outwards,  through  their  anterior  roots, 

FIG.  44. 


A      '1~~    A 

TRANSVERSE    SECTION    OF   THE    SPINAL    CORD    AND    ROOTS    OF   THE 
SPINAL    NERVES    OF   A    CAT. 


A  Anterior  roots. 
P  Posterior  roots. 
U  Compound  nerve  formed  by  the 

junction  of  these  roots. 
b   Branches  given  forth  from  the 

united  nerve. 


1  Anterior  (or    ventral)   median 

fissure  of  spinal  cord. 

2  Posterior    (or   dorsal)    median 

fissure. 


to  the  nervous  fibres  which  pass  to  the  muscles  and 
excite  motion  in  them. 

Bnt  a  response  quite  independent  of  volition  may  also 
take  place  when  feeling  is  in  no  way  impaired.  Thus,  if 
a  small  object  be  placed  sufficiently  far  back  in  the 
mouth,  the  muscular  act  of  swallowing  will  be  performed 
automatically. 

It  is  evident,  as  before  said,  that  the  cat  can  feel 
pleasure  and  pain,  and  can  experience  a  variety  of 
definite  sensations  (of  sight,  sound,  odour,  <fec.),  which 


THE  LIVING   WORLD  227 

the  creature  can  so  employ  as  to  have  a  practical  sense- 
perception  (through  its  different  and  combined  senses) 
of  different  objects  which  it  also  practically  distinguishes 
from  itself. 

Feelings  experienced,  successively,  tend  to  become 
associated  together.  Thus  it  is  when  some  definite 
past  feeling  is  revived,  an  imagination  of  feelings,  and 
groups  of  feelings,  previously  associated  with  that  past 
definite  feeling,  will  again  present  themselves  to  the  cat's 
imagination,  and  create  expectant  feelings  as  well  as 
render  sense-perceptions  more  distinct  and  significant. 

It  is  impossible  to  doubt  that  a  cat  can  at  the  same 
time  see,  feel,  smell,  and  taste  a  mouse  it  has  caught,  as 
also  that  it  can  hear  its  cry  while  seeing  it  and  clawing 
it,  before  killing  it.  There  must,  therefore,  be  some 
common  centre  where  these  influences  are  simultaneously 
received.  There  is  no  reason  to  suppose  the  cat  can 
know  that  it  exists  and  that  it  is  not  the  mouse,  but  it 
evidently  possesses  a  feeling,  however  vague,  of  this 
distinction.  This  feeling  of  self-identity  and  distinct- 
ness from  other  things,  is  to  be  distinguished  as  a  feeling 
of  consentience.  That  the  cat  possesses  a  power  of  retain- 
ing and  reproducing  groups  of  feelings  which  have  before 
been  excited  in  it  by  external  objects,  can  hardly  be 
doubted,  since  dogs  give  sometimes  such  plain  signs  that 
they  dream,  and  dreams  are  the  reproduction,  by  imagina- 
tion, of  sense-perceptions  previously  experienced.  The 
cat  has  also  the  power  of  associating  effects  of  past 
sensations  with  present  ones  in  such  a  ^vay  that  the 
occurrence  of  one  will  excite  the  other.  We  cannot 
doubt  that  the  sound  of  a  gnawing  mouse,  or  a  percep- 
tion of  its  odour,  will  excite  in  the  cat's  imagination 
an  image  of  a  mouse,  and  this  may  lead  it  to 
intensify  the  exercise  of  its  senses  and  so  simulate  what 


228  ELEMENTS   OF   SCIENCE 

we  know  as  "attention."  This  implies  that  the  animal 
possesses  a  certain  power  of  memory,  though  no  one 
supposes  that  the  cat  notices  its  own  recollections,  as 
such,  or  ever  sets  itself  to  try  and  recall  something 
temporarily  forgotten.  Similarly,  though  the  animal 
does  not  note  that  objects  are  of  certain  shapes  and 
sizes,  that  they  are  few  or  many,  that  they  are  in  a 
particular  place  or  that  they  move  and  so  change  their 
relative  positions,  nevertheless,  its  faculties  enable  it  to 
practically  respond  to  the  different  feelings  induced 
by  all  such  external  relations  which  exist  between 
it  and  surrounding  things.  The  cat  acts  differently 
according  as  only  one  mouse  or  two  mice  are  present, 
and  according  as  a  mouse  is  still  or  is  running  away, 
and  it  regulates  its  movements  of  pursuit  according  to 
the  changing  relations  which  the  mouse's  flight  gives 
rise  to,  between  the  mouse  itself  and  the  pieces  of 
furniture  in  a  room  through  which  it  tries  to  escape. 
The  cat  may  also  experience  surprise,  feel  '  puzzled 
and  have  its  attention  strongly  excited,  without  being 
aware  of  those  experiences  as  such.  Similarly  it  will 
with  amazing  rapidity  take  means  to  effect  a  desired 
end,*  sometimes  by  jumping  to  undo  the  latch  of  a  door ; 
but  it  does  this  without  recognising  that  it  is,  in  fact, 
taking  means  to  effect  an  end.  By  such  movements  it 
really  acts  as  a  cause  producing  an  effect,  but  it  does  not 
regard  itself  as  a  cause  or  recognise  effects  produced  by 
it  as  being  what  they  are. 

Again  the  experience  of  some  slight  sensations  which 
have  often  before  occurred  as  preliminaries  to  other 
vivid  ones,  and  have  so  become  associated  therewith — as 
a  jingle  of  cups  preliminary  to  the  experience  of  a  saucer 

*  See  "The  Cat,"  pp.  365-371. 


THE   LIVING  WORLD  229 

full  of  milk — will  give  rise  to  an  expectant  feeling* 
which  is  often  subsequently  gratified ;  but  this  does  not 
imply  that  the  cat  mutely  says  to  itself,  "  Sounds  of  cup 
jingling  are  probable  preliminaries  to  milk  tasting.  The 
sounds  I  hear  are  cup  jinglings,  therefore  the  sounds  I 
hear  are  probable  preliminaries  to  milk  tasting." 

Finally,  the  cat  has  a  certain  vocal  language  and  a 
language  of  gesture.  That  is  to  say,  it  emits  different 
sounds  according  to  the  feelings  it  experiences,  mewing, 
purring  and  spitting  as  the  case  may  be.  The  gesture 
language  of  a  cat  to  a  beloved  mistress  is  often  very 
expressive  of  attachment,  while  the  gestures  it  will 
exhibit  to  a  threatening  dog  are  unmistakable  indeed. 
The  cat  by  the  sounds  it  emits,  or  the  gestures  it  makes, 
has  the  power  of  so  giving  rise  to  corresponding  feelings 
in  other  creatures  that  the  latter  can  often  practically 
understand  what  it  means,  as  the  cat  can  understand,  to 
the  same  extent,  the  meaning  of  the  sounds  and  gestures 
of  a  threatening  dog.  Such  language  may  therefore  be 
called  a  language  of  feeling  or  "emotion." 

The  cat  has  also  the  power  of  acquiring  certain  habits. 
Now  a  habit  is  a  curious  and  interesting  thing.  A 
"  habit "  is  not  formed  by  repeating  actions,  "though  it 
may  be  strengthened  by  them.  If  an  act  performed 
only  once  had  not  in  it  some  power  of  generating  a 
"habit,"  a  thousand  repetitions  would  not  generate  it. 
Most  animals  (certainly  such  an  animal  as  the  cat)  have 
a  natural  tendency  to  activity — a  positive  want  of  it. 
An  animal's  powers  also  tend  to  increase  with  activity 
(within  limits)  and  dimmish  with  too  prolonged  repose. 
Habit  is  then  the  determination  in  one  direction  of  a 
previously  vague  tendency  to  activity. 

*  See  ante,  p.  227, 


230  ELEMENTS   OF   SCIENCE 

But  the  cat  also  possesses  instincts.  The  action  by 
which  the  kitten  first  sucks  the  nipple  and  swallows  the 
thence  extracted  nutriment  are  instinctive  actions. 
They  are  necessary,  definite  actions  which  have  never 
been  learned  but  are  performed  prior  to  all  experience. 

Every  one  knows  that  kittens  more  or  less  resemble 
one  or  other  of  their  parents.  This  transmission  of 
parental  characteristics  is  called  heredity,  and  is  evi- 
dently a  property  of  the  parents  which  transmit  their 
likeness.  Unusual  peculiarities,  such  as  additional  toes 

FIG.  45. 


THE    RIGHT   WHALE. 

and    claws,    are    characters    which    also    tend    to    be 
inherited. 

Such  is  the  cat,  and  a  variety  of  beasts — lions,  tigers, 
leopards,  lynxes,  &c. — are  formed  almost  entirely  in  the 
same  manner,  save  as  regards  size.  Other  beasts  differ 
from  it  in  greater  or  lesser  degrees,  till  we  come  to 
such  forms  as  bats  and  monkeys,  whales  and  porpoises. 
A  monkey  or  ape  is  formed  much  like  a  cat,  but  the 
proportions  and  shape  of  the  paws  and  toes  are  very 
different,  and  the  same  is  the  case,  though  to  a  less 
degree,  with  the  limbs.  The  teeth,  also,  are  very 
different.  They  are  suitable  for  eating  fruits,  not 
for  cutting  and  dividing  flesh.  There  are  various  other 
orders  of  beasts,  all  of  which  resemble  the  cat  more 


THE   LIVING   WORLD  231 

closely  than  they  do  any  bird,  reptile,  or  fish.  In  birds, 
we  meet  with  very  beautiful  structures — feathers — 
which  are  found  in  no  animal  which  is  not  a  bird ;  and 
large  feathers  are  almost  always  present  in  the  wings 
and  tail.  There  are  nearly  11,000  different  kinds  of 
birds,  but  they  are  all  formed  much  on  the  same  model, 
FIG.  46. 


THE    RHINOCEROS    VIPER. 

the  difference,  e.g.,  between  a  nightingale  and  a  goose, 
being  slight  indeed,  compared  with  those  which  exist 
between  a  horse  and  a  squirrel  amongst  beasts,  or 
between  a  tortoise  and  a  snake  in  the  great  group  of 
reptiles. 

As  we  all  know,  parrots  and  some  other  birds  will 
karn  to  articulate  words  and  sentences  with  great 
distinctness,  without,  of  course,  understanding  the 


232 


ELEMENTS   OF   SCIENCE 


signification  of  the  words  to  which  they  give  utterance, 
and  which  they  evidently  take  pleasure  in  repeating. 

All  birds  have  two  pairs  of  limbs,  but  many  reptiles 
have  none,  and  serpents  creep  over  the  ground  by  the 
aid  of  their  numerous  and  very  movable  ribs,  while  their 

FIG.  47. 


THE  DEVELOPMENT  OF  THE  FROG  FROM  THE  TADPOLE. 

1  to  7,  successive  stages.    2,  with  external  gills,  which  have 
disappeared  in  3. 

excessively  distensible  jaws  enable  them  to  swallow 
creatures  of  very  large  size,  compared  with  that  of  their 
own  head  and  neck. 

Reptiles  are  not  normally  able  to  raise  the  tempera- 
ture of  their  bodies  above  that  of  the  atmosphere  they 


THE   LIVING  WORLD 


233 


live  in,  but  birds  are,  as  before  said,  very  hot-blooded, 
their  warmth  being  promoted  by  the  fact  that  air  passes 
from  their  lungs  into  different  parts  of  their  bodies, 
sometimes  even  into  the  substance  of  almost  all  their 
bones. 

Frogs  and  toads  are  animals  which,  in  their  young 

FIG.  47. 

4 


THE  DEVELOPMENT  OF  THE  FROG  FROM  THE  TADPOLE. 

4  and  5  show  the  limbs  growing  out :  6  and  7  the  tail  very  nearly 
and  quite  absorbed. 

condition,  possess  a  power  which  has  not  yet  been 
noticed.  Their  young,  called  tadpoles,  are  aquatic  and 
do  not  at  first  breathe  at  all  by  lungs,  but  by  the  inter- 
vention of  delicate  processes  of  skin  which  are  placed  on 
either  side  of  the  neck  and  which  float  in  the  water, 


234  ELEMENTS   OF   SCIENCE 

Such  structures  are  termed  gills,  and  in  them  the  blood 
exchanges  its  carbonic  acid  for  oxygen,  as  it  does  in  the 
lungs  of  the  cat  and  other  beasts.  It  is  not  that  the 
water  is  dissolved  into  oxygen  and  hydrogen.  The 
oxygen  absorbed  is  gained  from  air  which  is  mixed  up  * 
in  the  water.  When  this  air  has  been  expelled  by 
boiling  the  water,  no  animal  with  gills  can  any  longer 
live  in  it.  Adult  frogs  and  toads  have  no  gills  but  lungs, 
by  which  they  breathe,  as  is  the  case  with  almost  all 
their  tailed  relatives,  the  efts,  and  as  all  the  higher 
animals  do. 

The  immense  group  of  fishes    all   breathe   by   gills, 


FIG.  48. 


THE   EFT    AMBLYSTOMA. 

though  a  few  kinds  also  possess  an  apparatus  for  breath- 
ing air  which  is  more  or  less  comparable  with  a  lung. 

Beasts,  birds,  reptiles,  frogs,  and  their  allies,  with 
fishes,  make  up  the  great  group  (class)  of  vertebrate,  or 
back-boned,  animals. 

We  can  here  only  refer  to  two  other  great  sub- 
kingdoms,  referring  the  reader  for  all  else  to  works 
devoted  to  zoology. 

The  first  of  these  is  far  richer  in  the  number  of  kinds 
it  contains  than  are  all  the  other  classes  of  animals 
taken  together.  It  is  the  sub-kingdom  Arthropoda, 

*  See  ante,  p.  153, 


THE    LIVING  WORLD  235 

which  embraces  all  insects,  hundred  and  thousand  legs, 
scorpions,  spiders,  tics,  and  inites,  all  lobsters,  crayfish, 
crab  and  shrimp-like  creatures.  As  an  example,  we  may 
select  the  crayfish,  the  body  of  which  is  evidently  in 
part  composed  of  a  longitudinal  series  of  similar  seg- 
ments, while  numerous  pairs  of  lateral  appendages 
successively  appear  (from  before  backwards)  as  feelers, 
jaws,  claws,  feet,  and  swimming  paddles. 

There  are  two  conspicuous  eyes,  each  borne  on  a  stalk. 
A  nervous  system,  composed  of  longitudinal  bands  and 

FIG.  49. 


CRAYFISH  (Actacus  fluviatiUs). 

ganglia,  runs  along  the  body  inside  its  lower  or  ventral 
surface,  whereas  in  vertebrates  it  is  situated  in  the 
dorsal  region  or  back.  It  is  there,  in  the  crayfish, 
that  the  heart,  a  single-chambered  organ,  is  placed, 
whence  blood-vessels  proceed,  the  blood  being  purified 
by  the  aid  of  gills  which  project  upwards  from  the  bases 
of  the  legs.  In  this  form  of  body,  serial  symmetry  is 
carried  to  a  far  greater  extent  than  in  vertebrate 
animals,  while  bilateral  symmetry  is  no  less  obvious. 

The  class  of  insects  are  remarkable  for  their  power  of 
flight;  but  their  wings  have  no  resemblance,  save  as 
regards  the  function  they  perform,  to  the  wings  of 
vertebrate  animals,  whether  bats  or  birds.  Insects 


236  ELEMENTS   OF   SCIENCE 

breathe  air,  but  not  by  lungs.  Instead  of  one  windpipe, 
they  have  many,  which,  opening  on  different  parts  of  the 
external  surface  of  the  body,  ramify  inwards,  and  carry 
air  (for  respiration)  to  all  parts  of  the  frame.  Scorpions, 
however,  do  not  thus  breathe,  but  by  means  of  a  series 
of  small  sacs,  which  open  in  the  under  surface  of  the 
body  and  admit  air  within  them.  The  jaws  of  arthro- 
pods are  quite  different  from  those  of  vertebrates,  and 


a 

THE  SNAIL  (Helix  pomatia). 


a     The  hinder  termination  of  the 

intestine. 

ga  Generative  aperture. 
I     Lip. 


p  '  Shell  margin. 

pi"  Respiratory  aperture. 

t'     So-called  olfactory  tentacle. 

t     Eye  tentacle. 


«     Shell. 

(After  Howes.} 

bite  laterally,  and  neither  from  above,  downwards,  nor 
from  before  backwards. 

The  other  sub-kingdom  to  be  noticed  here,  is  that  of 
the  molluscs  (Mollusca),  and  embraces  all  snails,  whelks, 
cuttle-fishes,  oysters,  mussels,  &c.  Almost  all  of  them 
breathe  in  water  by  means  of  gills,  but  a  few,  as  the 
snails,  perform  aerial  respiration  by  the  aid  of  a  small 
sac  which  admits  air  within  it. 

The  snail  is  an  organism  which  contrasts  greatly  with 


THE    LIVING   WORLD 


237 


FIG.  51. 


an  arthropod.  Instead  of  a  succession  of  jointed  limbs, 
the  animal  moves  upon  a  single,  elongated,  muscular 
expansion,  called  the  foot.  Indeed,  serial  symmetry  is 
almost  abolished,  the  viscera  being  arranged  in  a  spirally 
coiled  projection  upwards  from  the  foot,  and  this  projec- 
tion is  protected  by  a  similarly  coiled  calcareous  shell. 
There  is  a  well-developed  head, 
with  two  pairs  of  retractile  pro- 
cesses, the  larger  of  which  bear 
eyes.  On  the  right  side  of  the 
animal,  close  to  the  anterior 
edge  of  the  shell,  is  a  large 
aperture  which  is  that  of  the 
breathing  sac.  There  are  no 
jaws,  like  those  either  of  a  ver- 
tebrate or  an  arthropod,  but 
within  the  mouth  there  is  a 
crescent  -  shaped  plate  above, 
and  a  cartilaginous  cushion  or 
pad,  bearing  teeth,  below. 

The  nervous  system  is  in  the 
form  of  a  ring  of  nervous 
tissue  round  the  gullet  with 
ganglia,  whence  nerves  proceed 
to  a  third  pair  of  ganglia. 

The  cuttlefish  is  like  a  snail 
devoid  of  an  external  shell  and 
with  the  body  not  spirally 
coiled,  while  the  margins  of  the  foot  are  drawn  out  into 
long  sucker-bearing  arms,  the  eyes  being  sessile.  It 
is  furnished  with  a  pair  of  gills  formed  somewhat  like 
those  of  the  lobster,  and  the  main  ganglia  of  its  nervous 
system  are  protected  by  a  sort  of  cartilaginous  skull. 

The  oyster,  mussel,  and  their  allies  mainly  resemble 


CUTTLEFISH  (Sepia). 


238  ELEMENTS   OF   SCIENCE 

the  snail  in  structure,  but  with  the  following  exceptions  : 
there  is  no  head  and  no  air  sac,  but  there  are  plate-like 
gills,  and  the  shell,  instead  of  being  a  single,  spirally 
coiled  cone,  consists  of  two  lateral  halves,  united  dorsally 
by  a  hinge,  and  bearing  to  the  creature  between  them, 
somewhat  the  relation  of  the  two  sides  of  a  frock  coat  to 
the  man  who  wears  it. 

Having,  it  is  hoped,  now  said  enough  to  stimulate  our 
readers  to  have  recourse  to  works  on  zoology  in  order  to 
pass  beyond  a  mere  introduction  to  the  elements  of  that 
science,  we  may  revert  to  general  considerations  which 
refer  to  the  whole  of  the  organic  or  living  world. 

We  have  already  seen*  what  are  the  properties  of  that 
substance,  protoplasm,  which  is  common  to  all  animals 
and  plants,  but  the  simplest  facts  of  physiology  suffice  to 
establish  the  great  distinction  between  the  living  and  the 
non-living  world.  A  seed,  under  suitable  conditions,  will 
give  rise  to  a  plant  which  will  again  prod  Lice  a  seed,  and 
from  the  kitten  there  will  similarly  be  produced  a  cat, 
and  thence  a  kitten  once  more.  So  the  changes  of 
organic  life  tend  to  recur  in  cycles — the  necessary  condi- 
tions of  heat,  moisture,  and  gaseous  material,  &c.,  being 
supplied.  Thus  the  existence  of  an  innate  tendency  to 
go  through  a  definite  cycle  of  changes  when  exposed  to 
certain  fixed  conditions,  forms  a  distinction,  not  only 
between  mineral  substances  and  living  organic  bodies, 
but  also  between  living  organisms  and  those  which  have 
died.  The  latter  will  go  through  changes  indeed,  but  not 
a  cycle  of  changes— they  never  return  to  the  point  whence 
they  set  out. 

Inorganic  substances  tend  simply  to  persist  as  they 
are,  and  have  no  definite  relations  either  to  the  past  or 

*  See  ante,  pp.  192-197. 


THE   LIVING   WORLD  239 

to  the  future.  But  every  living  creature,  at  every  stage 
of  its  existence,  regards  both  the  past  and  the  future,  and 
thus  lives  continually  in  a  definite  relation  to  both  of 
these,  as  well  as  to  the  present.  It  has,  therefore,  under 
the  conditions  necessary  for  life,  a  definite  spontaneous 
activity  of  its  own.  An  inorganic  body  may  be  one  kind 
of  substance,  but  it  is  only  a  living  organism  which  can 
be  called  an  individual.  As  yet  science  has  not  afforded 
us  any  means  whereby  we  may  give  origin  to  life — 
whereby  we  may  change  any  non-living  substance  into 
a  being  instinct  with  life. 

Plants  possess  the  power  of  performing  all  the  functions 
essential  to  continued  life — namely,  alimentation,  circula- 
tion, respiration,  secretion  and  generation.  They  give 
no  evidence,  however,  of  possessing  any  true  power  of 
sensation.  The  movements  of  the  sensitive  plant,  the 
sun-dew,  Yenus's  fly-trap,  &c.,  are  very  wonderful,  but 
the  most  careful  examination  of  those  plants  has  not 
discovered  any  nervous  tissue  in  them.  As  this  is  the 
essential  and  only  organ  of  feeling  which  organisms  are 
known  to  possess,  its  absence  in  plants  justifies  our 
denying  them  the  power  of  sensation.  To  say  that  our 
ordinary  domestic  plants — our  potatoes,  and  our  cabbages 
— really  feel,  would  be  absurd  in  the  eyes  of  men  of 
common  sense. 

The  movements  of  plants  are  also  effected  in  a  different 
manner  from  those  of  animals.  In  the  latter  it  takes 
place  by  the  aid^of  muscular  tissue,  a  substance  which 
has  not  yet  been  found  in  any  plant,  and  it  is  a 
rule,  gathered  from  long  experience,  that  "structure"  and 
"  function,"  in  organisms,  vary  together. 

As  already  pointed  out,  no  animal  can  live  without 
feeding,  directly  or  indirectly,  upon  plants,  since  they 
alone  possess  the  power  of  building  up  organic  matter 


240  ELEMENTS   OF   SCIENCE 

directly  from  the  inorganic  world.  With  the  exception 
of  fungi  and  some  parasitic  plants  (such  as  the  dodder), 
the  whole  vegetable  world  is  continually  engaged,  during 
the  hours  of  daylight,  in  tearing  from  the  atmosphere 
its  carbon,  and  in  absorbing  moisture  in  order  to  build 
up  substances  capable  of  life. 

The  repair  of  injuries  and  reproduction  of  lost  parts 
take  place  in  lower  animals  to  a  much  greater  extent 
than  it  does  in  the  one  selected  as  our  type — the  cat. 
The  tails  of  lizards,  the  limbs  of  efts,  and  the  legs  and 
claws  of  lobsters,  if  broken  off,  will  be  reproduced,  and 
some  aquatic  worms  have  been  cut  into  as  many  as 
twenty-five  parts,  with  the  result  that  each  separated 
part  has  grown  into  a  whole.  Some  polyp-animals 
form  buds  (like  those  before  spoken  of  as  being  pro- 
duced by  tiger  lilies),  which  will  often  become  detached, 
and  then  grow  up  into  new  individuals,  like  those  plants 
which  will  give  forth  "  suckers "  and  then  separate. 
The  common  bramble  will  attach  itself  to  the  ground 
by  the  end  of  a  "shoot,"  rootlets  coming  to  take  the 
place  of  the  incipient  leaves  of  its  terminal  bud,  and 
so  a  new  stem  is  formed. 

Thus  "growth"  is  " continuous  reproduction,"  and 
"  reproduction "  is  a  form  of  growth  which  may  be 
"continuous"  or  "discontinuous."  Continuous  repro- 
duction occurs  in  animals  as  well  as  in  plants,  and  thus 
it  is  that  many  coral  animals  grow  up  as  arborescent 
structures,  or  into  large  masses  leading  to  the  formation 
of  reefs  and  islands.  Discontinuous  growth  may  occur 
in  certain  worms,  which  habitually  divide  themselves  and 
so  multiply,  and  multitudes  of  Protozoa,  as  before  said, 
multiply  by  spontaneous  fission. 

The  circuitous  course  of  development  of  the  embryo, 
before  mentioned  as  taking  place  in  the  kitten,  is  pursued 


THE   LIVING   WORLD  241 

to  a  greater  or  less  extent  in  the  development  of  almost 
all  animals. 

The  embryos  of  higher  animals  for  the  most  part 
transitorily  resemble,  in  their  general  features,  the 
structure  of  other  animals  lower  in  the  scale.  The  series 
of  forms,  also,  through  which  the  embryo  of  a  higher 
animal  passes  in  its  development  (or  ontogeny),  succes- 
sively resembles,  in  a  general  way,  a  series  of  adult  forms 
of  animals  lower  in  the  scale  of  life. 

Thus  the  heart  of  a  cat  is  at  first  but  a  single  tube,  as 
it  permanently  remains  in  the  ascidians  or  sea  squirts. 
The  cat's  brain  consists  in  its  earliest  stages  of  a  series  of 
simple  vesicles,  roughly  like  the  brain  of  that  lowly  fish, 
the  lamprey.  In  a  more  advanced  stage,  the  embryo  of 
the  cat  is  plainly  the  embryo  of  a  beast — not  of  a  fish — • 
and  later  on  it  is  plainly  that  of  some  beast  of  prey. 

Most  remarkably  obvious  are  those  changes  which  take 
place  when  the  embryo  is  a  free  active  creature  during 
its  development. 

Thus  the  young  of  the  frog  is,  as  before  said,  a 
tadpole,  and  so  the  frog  in  its  development  is  said  to 
undergo  a  metamorphosis.  No  less  marked  is  that  change 
which  most  insects  undergo,  and  which  is  so  well  seen  in 
butterflies  and  moths,  which  are  first  actively  feeding 
grubs,  then  quiescent  crysalides,  and  finally  reproductive, 
usually  winged,  adults.  These  stages  are  known  in 
zoology  as  (i)  the  larva  ;  (2)  the  pupa  ;  and  (3)  the  imago 
or  the  perfect  and  mature  insect. 

Thus  the  whole  of  the  living  organic  world  begins,  as 
it  were,  from  a  common  unicellular  starting-point,  whence 
the  two  kingdoms  of  organic  life  may  be  said  to  diverge. 
The  animal  kingdom  advances  in  complexity  from  a 
structure  resembling  a  double-walled  sack,  with  a  per- 
manent digestive  cavity,  and  possessing  nervous  and 


242  ELEMENTS   OF   SCIENCE 

muscular  tissue — such  a  condition  we  find  in  the  hydra. 
The  vegetable  kingdom  advances  in  complexity  in  a 
quite  diverse  mode,  building  up  a  variously  branching 
axis  with  foliar  organs  (modified  leaves),  but  always 
devoid  of  any  alimentary  cavity  and  any  form  of  muscu- 
lar or  nervous  tissue. 

The  functions  which  are  peculiar  to  the  higher  organ- 
isms, and  are  exhibited  by  all  living  creatures  which 
possess  nervous  and  muscular  tissue,  are  (as  has  been 
before  said)  those  of  movement  and  feeling.  These  two 
functions  are  distinguished  as  the  functions  of  animal  life, 
in  contradistinction  to  the  functions  of  nutrition  and 
reproduction,  which,  being  possessed  by  all  plants,  as 
well  as  animals,  are  termed  the  vegetative  functions. 
That  the  animals  with  which  we  are  most  familiar  have 
feelings  and  emotions,  and  that  we  can,  to  a  considerable 
extent,  tell  what  these  are,  hardly  any  one  will  be  dis- 
posed to  deny.  As  to  lower  animals,  the  complex  social 
economy  of  bees  is  a  matter  of  common  knowledge. 
Ants  display  a  complete  and  yet  more  complex 
political  organisation.  Some  have  soldiers  which  cap- 
ture slaves,  while  other  kinds  will  retain  other  insects 
(Aphides*)  captive  to  serve  a  purpose  analogous  to  that 
of  our  milk -giving  cattle. 

We  have  already  spoken  of  the  vocal  and  gesture 
language  of  the  cat.  Pointers  and  setters  will  make 
certain  facts  known  by  their  gestures;  the  songs  of 
birds  have  meanings  practically  understood  by  their 
fellows,  while  parrots  and  jackdaws  can  learn  to  articu- 
late whole  sentences. 

As  to  the  mental  faculties  of  the  higher  animals,  they 

*  The  small  slow-moving  green  flies  so  common  on  rose  trees 
and  pelargoniums. 


THE  LIVING  WORLD  243 

inay  be  astonished,  but  they  have  no  recollection  of  being 
astonished.  They  can  distinguish  an  artificial  object 
from  the  natural  object  which  it  imitates,  but  they  do 
not  understand  the  artificial  character,  as  such,  of  the 
former.  A  dog  may  fear  another  dog  which  is  stronger 
and  fiercer,  but  it  will  have  no  idea  of  "  courage "  and 
"  fierceness."  Many  animals,  even  insects,  will  distin- 
guish clearly  between  differently  coloured  objects — the 
white  from  the  blue,  the  red  from  the  yellow — but  no 
animal  gives  us  evidence  that  it  knows  "  whiteness  "  or 
"  blueness,"  and  still  less  that  it  knows  what  "colour" 
is.  Some  animals  also  have  feelings  of  sympathy,  com- 
panionship, regretful  feelings,  feelings  of  shame,  &c., 
but  we  have  no  ground  for  supposing  they  understand 
the  conceptions  "  ought  "  and  "  duty."  Animals  gene- 
rally possess  the  faculty  of  forming  "  habits,"  but  the 
instinctive  powers  of  many  of  them  are  much  greater 
than  those  of  the  cat.  Chickens,  two  minutes  after  they 
leave  the  egg,  will  follow  with  their  eyes  the  movements 
of  crawling  insects,  and  peck  at  them,  judging  distance 
and  direction  with  almost  infallible  accuracy.  They  will 
also  instinctively  appreciate  sounds,  readily  running  to- 
wards a  hen  hidden  in  a  box  when  they  hear  her  "  call." 
Some  birds  will  feign  lameness  in  order  to  draw  oft' 
attention  from  their  eggs  and  young,  and  birds  of  the 
first  year  will  readily  migrate  to  avoid  a  cold  of  which 
they  can  have  no  knowledge.  But  it  is  insects  which 
possess  the  most  remarkable  instincts,  such  as  those  of  the 
carpenter  bee,  the  wasp  sphex,  and  the  Emperor  moth, 
and  many  others,  for  a  description  of  which  the  reader 
is  referred  to  works  on  zoology,  and  especially  to  those 
on  entomology — the  natural  history  of  insects.  Such 
phenomena  make  it  clear  that  insects  will  make 
elaborate  arrangements  for  a  progeny  they  can  never 


244  ELEMENTS   OF   SCIENCE 

see,  and  the  habits  and  food  of  which  differ  widely  from 
those  of  the  parent  since  its  larval  condition.  We 
cannot  think,  however,  that  the  insect  possesses  any 
recollection  of  that  condition  so  that  its  parental  actions 
are  guided  thereby. 

As  we  said  in  the  beginning  of  the  chapter,  organisms 
have  definite  relations  (i)  to  time ;  (2)  to  space;  and  (3) 
to  one  another. 

As  to  time,  it  is  widely  known  that  some  animals  have 
become  extinct.  Thus  the  wolf  has  disappeared  from 
England  since  the  days  of  Henry  VIII.,  while  the 
bustard  has  ceased  to  exist,  although  eighty  years  ago  it 
wandered  over  the  South  Downs  and  Salisbury  Plain. 
Similarly,  plants  once  common  in  certain  places  have 
since  vanished,  as  the  many  peculiar  plants  of  St.  Helena 
have  been  almost  entirely  destroyed  by  the  rabbits  and 
goats  introduced  into  that  island. 

The  evidences  we  possess  of  past  organic  life  is  afforded 
us  by  the  five  kinds  of  fossils  before  described.*  This 
record  is  an  exceedingly  imperfect  one,  remains  of 
animals  and  plants  having  been  only  here  and  there 
exceptionally  preserved  by  some  favouring  accidents, 
and  often  in  a  very  fragmentary  manner.  The  study  of 
these  organic  remains  constitutes  the  science  of 
Palaeontology,  and  we  must  refer  our  readers  to  treatises 
on  that  science  for  further  information.  Here  we  will 
only  say  that  in  the  primary  rocks  have  been  found 
many  remains  of  echinoderms,  molluscs,  arthropods  and 
fishes. 

In  the  secondary  strata  we  find  evidences  that  great 
numbers  of  huge  reptiles  existed,  some  grazing  or  feed- 
ing on  trees,  and  others  of  most  predacious  habits. 

*  See  ante,  p.  170. 


THE   LIVING   WORLD 


245 


Then  our  present  whales  and  porpoises  were  anticipated 
by  gigantic  marine  reptiles,  ichthyosauri  and  plesiosauri, 
while  numerous  flying  reptilian  forms,  small  and  large, 
flitted  through  the  air  as  bats  do  now.  That  time 
may  well  be  called  the  age  of  reptiles.  Nevertheless, 
small  beasts  had  then  already  begun  to  make  their 
appearance. 

In  early  tertiary  times  creatures  existed  which  more 
closely  resemble  forms  now  living,  while  in  the  later 
tertiaries  are  entombed  the  remains  of  organisms  more 

FIG.  52. 


ICHTHYOSAURUS. 

Showing  the  outline  of  the  dorsal  and  tail  fins,  the  existence  of 
which  has  been  recently  discovered. 

and  more  like  those  now  living  as  we  examine  strata 
later  in  date. 

That  living  organisms  have  definite  relations  to  space 
has  been  already  noted  and  some  examples  given. 

Each  large  portion  of  the  earth's  surface  has,  in  fact, 
its  special  plant  population  or  flora,  as  it  has  its 
special  animal  population  or  fauna.  For  details  the 
student  is  referred  to  works  on  organic  geography. 
Nevertheless  it  may  here  be  noted  that  (i)  South 
America,  (2)  Africa  south  of  the  Sahara,  (3)  Australia 
and  (4)  India  with  its  Archipelago,  have  each  an  in- 
teresting and  peculiar  fauna ;  as  also  that  (5)  North 


246  ELEMENTS   OF   SCIENCE 

America  on  the  one  hand,  and  (6)  Europe,  with  North 
Africa  and  Asia,  on  the  other,  are  similarly,  though  less 
strikingly,  characterised.  Various  species  which  now 
inhabit  one  or  other  of  those  areas  closely  resemble 
certain  tertiary  fossils  also  found  therein. 

The  botanical  regions  into  which  the  world  is  divisible 
are  ten  in  number,  (i)  Arctic;  (2)  Boreal  (or  Europe, 
Asia  and  America,  from  the  Arctic  circles  to  the  Pyrenees, 
the  Alps,  the  Balkans,  the  Himalayas  and  North  America 
to  the  tropic  of  Cancer) ;  (3)  Caucasia,  or  the  shores  of 
the  Mediterranean  up  to  the  Pyrenees,  Alps,  and  Balkans, 
with  North  Africa  and  North-Western  Asia ;  (4)  Ethio- 
pia or  Africa  southwards  to  the  tropic  of  Capricorn,  with 
Madagascar  and  Southern  Arabia ;  (5)  South  Africa  to 
the  Cape;  (6)  Indo- Malayan,  or  the  Indian  Archipelago  ; 
(7)  Australian;  (8)  Neotropical,  or  tropical  South 
America  and  the  West  Indies;  (9)  Patagonian,  or 
America  south  of  the  Southern  tropic ;  and  (10)  Antarctic, 
or  Kerguelen's  land. 

The  geographical  range  of  living  creatures,  even  of  the 
same  class,  is  often  most  unequal.  Thus  the  flame-bearing 
humming-bird  is  confined  to  the  crater  of  the  extinct 
volcano  Chiriqui,  in  America,  while  the  crow  ranges  over 
almost  the  whole  world  except  South  America.  Different 
animals  and  plants  are  obviously  influenced  as  to  their 
extent  of  range  by  their  different  requirements  as  to 
heat,  light,  moisture,  &c. 

Beside  geographical  distribution,  living  organisms  have 
a  vertical  or  Bathymetrical  distribution.  Thus  in  the 
tropics,  palm,  bananas,  &c.,  grow  luxuriantly  in  the  low- 
lands. At  a  moderate  elevation  they  give  place  to  ever- 
greens, then  these  to  a  belt  of  deciduous  trees,  then  we 
find  only  shrubs,  grasses,  Alpine  plants,  and  mosses.  The 
camel  is  an  animal  of  the  plains,  but  the  llama  will 


THE   LIVING   WORLD  247 

ascend  to  18,000  feet  in  the  Andes.  The  viper  is  found 
in  the  Alps  at  5000  feet  above  the  sea,  and  in  South 
America  the  condor  will  soar  to  more  than  22,000  feet 
above  the  sea-level. 

The  ocean  has  different  inhabitants  at  different  depths, 
and  there  seems  to  be  no  depth-limit  to  life,  especially 
to  animal  life.  At  a  depth  of  2000  fathoms  the  ocean 
fauna  present  much  richness  and  variety. 

As  to  the  inter-relations  of  living  organisms,  one 
great  organic  inter-relation,  already  noticed,  underlies  all 
others — namely  that  by  which  oxygen  is  set  free  by 
plants  to  be  made  use  of  in  respiration  and  so  recombined 
with  carbon — a  process  which  has  been  called  the  "  cir- 
culation of  the  elements." 

The  phenomena  of  parasitism  constitute  a  very  common 
relation  between  organisms,  parasites  being  generally 
more  or  less  inimical  to  their  hosts. 

Besides  the  evident  relation  of  "  enemies  "  and  "  rivals," 
organisms  may  also  directly  or  indirectly  benefit  other 
creatures. 

Thus  ants  and  the  bull's-horn  acacia  benefit  each 
other  directly.  The  plant  furnishes  food  and  lodging 
(in  special  cavities)  to  the  insects,  which  in  turn  are 
ready  to  rush  out  and  bite  furiously  any  animals 
which  attempt  to  injure  the  tree.  Organisms  may  be 
benefited  indirectly  by  others  which  destroy  the  enemies 
or  rivals  of  the  former.  Again,  services  may  be  rendered 
in  very  curious  ways.  Thus  barnacles,  which  fix  them- 
selves on  whales,  are  provided  with  an  extra  amount  of 
food  by  being  so  carried  about.  A  small  fish  has  also 
been  found  to  live  within  the  interior  of  a  sea-anemone, 
feeding  on  portions  of  the  latter's  food.  Birds  dissemi- 
nate seeds  which  they  have  swallowed,  and  sometimes 
do  so  by  carrying  them — or  the  eggs  of  small  animals — 


248  ELEMENTS   OF   SCIENCE 

in  the  mud  which  may  adhere  to  their  feet.  Many 
curious  arrangements  exist  by  which  the  access  of  insects 
to  flowers — which,  as  before  said,  they  accidentally  fer- 
tilise by  dusting  the  stigma  with  pollen — is  facilitated, 
and  others  whereby  the  approach  of  noxious  creatures  is 
prevented. 

Plants,  the  pollen  of  which  is  only  carried  accidentally 
by  the  wind,  may  have  each  of  their  pollen-grains 
furnished  with  a  membranous  expansion  which  facili- 
tates its  carriage. 

There  is  sometimes  a  curious  resemblance  between 
different  creatures,  which  goes  by  the  name  of  mimicry. 
Familiar  examples  of  mimicry  are  clear-winged  moths, 
which  may  be  readily  mistaken  for  bees.  One  of  the 
most  perfect  examples  of  mimicry  is  displayed  by  the 
insect  called  the  "walking  leaf,"  which  in  form  and 
colour  so  closely  resembles  a  leaf  that  it  is  difficult  to 
find  it  when  amongst  real  leaves,  and  thus  it  escapes 
its  enemies. 

Other  creatures,  called  "  bamboo-insects,"  resemble  a 
stick  of  bamboo,  and  this  the  more  because  they  have 
the  habit  of  hanging  with  their  long  legs  stretched  out 
unsymmetrically. 

Certain  African  species  of  those  plants  which  are 
called  euphorbias  so  greatly  resemble  some  American 
cacti,  that  it  is  difficult  to  believe,  when  out  of  flower, 
that  they  are  not  close  allies,  instead  of  being  plants 
which  belong  to  widely  different  groups. 

Very  many  animals  partake  of  the  colour  of  their 
usual  surroundings.  Thus,  desert  snakes  and  lizards  are 
generally  sand-coloured,  while  those  which  inhabit  trees 
are  green. 

Actual  changes  of  colour  sometimes  preserve  this 
harmony.  Thus  the  ptarmigan,  the  variable  hare,  the 


THE   LIVING   WORLD  249 

ermine  and  the  Arctic  fox  become  white  in  winter  and 
so  match  with  the  snow. 

Sometimes  creatures  will  change  colour  readily,  as  is 
the  case  with  the  chameleon  and  some  insects  ]  modifica- 
tions of  form  and  colour  often  attend  the  advent  of  the 

FIG.  53. 


TWO    PLANTS,    VERY    DIFFERENT   IN    NATURE,    WHICH    GREATLY 
RESEMBLE   EACH    OTHER   EXTERNALLY. 

A   A  cactus  (Cereus)  from  Brazil. 

B    A  spurge  (Euphorbia)  from  Africa. 

breeding  season,  with  vocal  manifestations,  such  as  of 
singing  birds,  croaking  frogs,  and  rutting  stags. 

The  environment  of  organisms  will  also  affect  them  in 
many  other  ways,  besides  their  colours.  Thus  the  use 
of  soft  food  seems  to  have  diminished  the  jaws  of  both 
civilised  men  and  their  pet  dogs.  English  oysters 
transported  to  the  Mediterranean  are  said  to  alter 
their  mode  of  growth  rapidly,  so  as  to  resemble  the 


250  ELEMENTS   OF   SCIENCE 

kind  natural  to  that  sea.  Setters  bred  at  Delhi  and 
cats  at  Mombas  in  Africa  have  been  known  to  undergo 
quickly,  or  in  a  generation,  considerable  modifications, 
while  twenty  kinds  of  American  trees  all  differ  from  their 
nearest  European  allies  in  a  similar  manner — less  toothed 
leaves,  fewer  branchlets,  &c. 

We  have  now  briefly  indicated  some  main  facts  which 
concern  living  creatures,  and  pointed  out  the  principal 
circumstances  whereby  they  differ  from  the  non-living 
world. 

We  must  next  direct  our  attention  exclusively  to  that 
highest  of  all  living  creatures  which  people  this  earth — 
our  own  species,  Man. 


CHAPTER  VII 
MAN 

THE  human  body  is  formed  on  the  same  fundamental 
type  of  structure  as  is  the  body  of  every  beast,  and 
therefore  that  of  the  cat  hereinbefore  briefly  described  ;* 
but  he  resembles  above  all  the  ape  in  structure,  so 
that,  thus  considered,  apes  and  men  may  be  said  to  stand 
together  on  a  sort  of  zoological  island,  widely  separated 
from  all  other  animals.  The  difference  in  structure 
between  an  ape  and  every  other  animal  is  very  much 
greater  than  that  which  exists  between  man's  body  and 
that  of  any  ape. 

All  races  of  men  are  very  similarly  formed.  Differ- 
ences exist,  as  everybody  knows,  with  respect  to  the 
colour  of  the  skin,  the  form  and  abundance  of  the  hair, 
the  prominence  of  the  jaws,  and  there  are  also  differences 
in  the  form  of  the  skull,  and  some  other  bony  structures, 
in  the  shape  of  the  chin,  and  in  the  muscular  and  fatty 
development  of  different  parts  of  the  body.  Neverthe- 
less such  differences  are  small  indeed,  when  compared 
with  those  which  exist  between  most  species  of  apes  and 
any  other  beasts  whatever. 

Similarly,  the  functions  which  the  human  body 
performs  are  similar  to  those  performed  by  the  body  of 
the  cat,t  and,  as  regards  the  nervous  system,  we  have, 

*  See  ante,  p.  217.  t  See  ante,  p.  221. 


252  ELEMENTS   OF   SCIENCE 

through  observations  on  injured  men,  the  best  evidence 
of  the  existence  in  them  of  "  reflex  action."  A  man 
whose  spinal  cord  has  been  greatly  injured  loses  all 
power  of  both  sensation  and  voluntary  motion  in  those 
parts  of  the  body  supplied  by  nerves  which  come  forth 
from  the  spinal  cord  below  the  place  of  injury.  At 
the  same  time  movements  of  those  very  parts  (often 
exaggerated  movements)  may  be  produced  by  pinching, 
burning  or  tickling  such  parts,  without  the  patient 
having  any  corresponding  feelings,  or  any  conscious- 
ness of  the  movements  which  he  may  see,  that  his  own 
limbs  are  thus  made  to  perform. 

But  while  the  nervous  system  of  man  ministers  to  all 
those  feelings,  single  and  associated,  which  result  in 
such  sense-perceptions  and  "  consentience*  "  as  the  cat 
possesses,  it  also  ministers  to  much  higher  powers 
than  those  which  any  beasts  possess.  We  can  describe 
a  beast,  but  no  beast  can  describe  a  man.  The  most 
important  difference,  then,  between  man  and  all  the 
other  objects  of  nature  we  have  yet  considered,  is  the 
difference  which  exists  between  his  power  of  conscious 
thought,  his  intellectuality,  and  all  the  powers  possessed 
by  any  other  creature  of  which  our  senses  can  give  us 
cognisance. 

The  study  of  this  intellectual  power  and  of  the  lower 
power  of  mere  feeling,  sense-perception,  &c.,  which 
accompany  it,  constitutes  a  distinct  study,  which  is 
usually  designated  Psychology.  This  study  not  only 
differs  greatly  from  all  other  studies,  as  regards  the 
object  to  which  it  is  directed,  but  it  differs  absolutely 
from  them  as  to  the  mode  in  which  alone  it  can  be 
carried  on.  In  every  other  study  our  attention  is 

*  See  ante,  p.  227. 


MAN  253 

directed  to  some  external  object  or  action,  but  in 
studying  psychology  we  have  to  direct  our  attention 
inwards  upon  our  own  thoughts  and  feelings,  and  upon 
the  actions  of  our  own  mind.  Feelings  and  thoughts 
can,  of  course,  be  directly  known  only  by  the  being  who 
has  them,  and  who  knows  that  he  possesses  them,  for 
without  such  knowledge  he  could  not  intentionally  and 
deliberately  examine  them. 

Now,  on  turning  our  mind  inwards,  we  can,  to  begin 
with,  recognise  two  very  distinct  kinds  of  mental 
activity.  Let  us  suppose  we  are  walking  through  a 
wood,  while  thinking  about  the  study  of  nature.  We 
may  then  recognise  that  a  series  of  thoughts,  of  which 
we  are  conscious,  has  been  passing  (as  the  phrase  goes) 
through  our  mind,  whil?,  at  the  same  time,  our  feet 
must  have  received  a  series  of  sense-impressions  from 
the  ground  walked  over,  to  which  sense-impressions  we 
paid  no  attention  at  all,  though,  when  we  advert  to  them, 
we  can  recognise  them  as  having  existed.  These  two 
orders  of  mental  activity,  (i)  sensations  and  (2)  thoughts, 
are  types  of  two  distinct  classes  of  mental  activities — two 
faculties  which  we  possess  ;  the  lower  of  these  is  our  sensi- 
tive activity  (a  faculty  which  we  share  with  other  animals), 
the  higher  is  our  intellectual  faculty,  which,  as  far  as  we 
have  been  able  to  ascertain,  is  one  possessed  by  no  other 
animal  whatever.  This  is  probably  the  most  fundamental 
and  important  of  all  the  distinctions  to  be  made  in  the 
study  of  the  mind ;  for  without  it  no  accurate  and  satis- 
factory knowledge  is  possible  of  what  the  mind  of  man 
really  is. 

Now,  in  the  first  place,  we  have  the  power  of  recog- 
nising the  existence  of  whatever  we  perceive  to  exist — 
to  recognise  that  it  really  exists,  to  recognise  its  being. 
This  idea,  the  idea  of  "  being,"  is  an  idea  which  we  must 


254  ELEMENTS   OF   SCIENCE 

possess  in  order  to  be  able  to  perform  any  intellectual 
act  whatever.     Most  persons  never  think  about  it,  and 
many  readers  may  be  surprised  that  they  have  had  it  all 
along   without  ever    recognising   it.     But   though  not 
itself  at  first  adverted  to,  it  is  by  that  idea  alone  that  all 
other  ideas  are  intelligible  to  us — as  light,  though  itself 
unseen,  makes  all  other  things  visible.     If  we  cannot 
perceive  that  anything  "is,"  we  cannot,  of  course,  perceive 
anything  at  all.     But  ordinarily,  and  especially  in  the 
beginning  of  our  intellectual   career,  our   attention   is 
directed  to  real  concrete  external  objects,  in  perceiving 
any  one  of  which  our  minds  acquire  two  distinct  expe- 
riences:   (i)  the  intellectual  apprehension  of  the  object 
perceived  ;  and  (2)  the  sensations,  ordinarily  unnoticed, 
which   serve   to  make    that   object  known   to   us.      If 
the  reader  will  consider  for  himself  the  action  of  his 
own  mind,  he  will  perceive  such  to  be  the  case ;  thus,  for 
example,  should  he,  when  reading  this,  have  lately  met 
a  carriage  with  some  friends  of  his  in  it,  let  him  ask 
himself  what  was  present  to  his  mind  at  the  time.     He 
will  say  that  the  presence  of  the  carriage  and  his  friends 
was  what  he  directly  perceived.     Of  course,  in  order  to 
perceive  them,  he  must  have  experienced  certain  sensa- 
tions :  his  eyes  saw  various  patches  of  different  colours, 
and  his  ears  heard  the  sound  produced  by  the  wheels, 
the  horse's  hoofs,  and  his  friends'  voices.     But  he  never 
adverted  to  these  sensations  at  the  time  he  felt  them, 
though  he  can  turn  his  mind  back  and  recognise  that 
they  were  then  present  to  his  sensitive  faculty.     His 
intellect  was  not  occupied  about  his  sensations  when  he 
perceived   his   friends,  so   that   his   sensations,  though 
affecting    his    sensitive   faculty,   were    not   themselves 
perceived.     Sensations  are  the  means,  not  the  object  of 
perception.     They  hide  themselves  from  our  notice,  in 


MAN  255 

giving  rise  to  the  perception  they  elicit.  They  can  only 
be  recognised  by  an  express  turning  back  of  the  intellect 
upon  them.  Ordinarily  they  remain  unnoticed,  and  we 
only  perceive  the  thing  they  reveal — things  they 
"  represent,"  in  the  sense  of  making  them  present  to  the 
intellect.  If  we  enter  a  library  we  do  not  see  "  images 
of  books  in  rows "  but  the  very  books  themselves. 
Perception  is  not  inference  from  sense-impressions ;  for, 
in  the  first  place,  we  do  not  attend  to  them,  while  if  we 
are  doubtful  about  any  object,  we  "make  sure"  of  it, 
not  by  any  reasoning  about  sensations,  but  by  merely 
tightening,  as  it  were,  our  sensuous  grasp  of  an  object 
and  focusing  our  sense-impressions  more  carefully. 
Intellectual  perception,  then,  is  a  natural,  spontaneous, 
and  unconsciously  made,  interpretation  of  sensible 
signs,  by  a  special  power  of  our  intelligence.  Such  an 
"interpretation"  is  an  act  of  mental  conception,  and 
"  concepts  "  are  the  simplest  elements  of  our  intellectual 
life.  A  concept  contains  implicitly  a  judgment.  Thus, 
e.g.,  the  concept  "  bright  sun  "  contains,  implicitly,  the 
explicit  judgment  <(  the  sun  is  bright "  and  explicit 
judgment  comes  next  after  concepts.  The  most  elemen- 
tary complete  acts  of  the  mind  are,  then,  explicit 
judgments,  which  are  acts  of  the  intellect,  as  it  were, 
itself  sitting  in  judgment  on  two  concepts,  and  pro- 
nouncing as  to  some  relation  which  exists  between 
them  —  as,  that  they  agree  or  disagree  :  in  fact 
stating  explicitly,  what  has  been  already  implicitly 
seen. 

Every  object  which  we  perceive,  possesses  a  number 
of  different  qualities— shape,  size,  colour,  hardness, 
&c.,  and  acts  on  our  sensibility  accordingly.  Now,  our 
attention  may  be  directed  to  various  qualities,  according 
to  the  different  circumstances  of  each  case,  and  then  these 


256  ELEMENTS   OF   SCIENCE 

qualities  may  be  distinctly  recognised  as  really  being 
qualities  of  the  object  observed. 

The  power  by  which  we  thus  ideally  separate  qualities 
is  called  abstraction,  and  by  it  our  mind  isolates  (in  order 
to  apprehend  them  distinctiy)  the  various  qualities  and 
conditions  which  really  exist  in  any  object  perceived. 
Thus  if  the  object  perceived  be  a  horse,  we  may  notice 
that  it  has  the  characters  of  "  a  quadruped,"  that  it  is 
"  a  living  creature,"  that  it  is  "  a  solid  body,"  or  at  least 
that  it  is  "  a  something."  Each  such  conception,  though 
applicable  to  a  multitude  of  individuals  of  the  same 
kind,  is  a  conception  which,  considered  in  itself,  is  one. 
It  is  a  single  notion,  not  of  any  one  separate  and  sub- 
sisting thing,  but  it  refers  to  a  group  of  objects,  to  each 
of  which  the  notion  is  applicable.  It  is  an  abstract  idea 
of  a  lower  or  higher  degree  of  abstraction ;  thus  the  term 
"  horse  "  is  an  abstract  idea  formed  through  all  we  may 
have  learned  about  horses.  The  term  quadruped  is  more 
abstract,  and  is  applicable  to  a  vastly  larger  group  of 
creatures.  The  same  is  again  the  case  with  the  abstract 
ideas  "  living  creature  "  and  "  solid  body,"  while  in  the 
idea  "  something,"  which  is  the  idea  of  "  being,"  we 
arrive  at  the  highest  possible  degree  of  abstraction,  the 
most  abstract  of  all  "  abstract  ideas." 

That  feelings  and  "ideas"  are  fundamentally  distinct,* 
is  shown  by  the  fact  that  the  same  idea  may  be  called  up 
in  the  mind  by  either  sight,  hearing,  or  feeling  (e.g.,  the 
idea  "  triangle  "),  while  one  set  of  sense  impressions  may 
give  rise  to  a  great  number  of  different  ideas,  as  the  sight 
of  a  single  photograph  of  the  Queen  may  give  rise  to  the 


*  The  reader  is  referred  for  much  further  information  on  this 
subject  to  our  work  entitled  "  The  Origin  of  Human  Reason." 
Kegan  Paul,  Trench  &  Co.,  1889,  p.  45. 


MAN  257 

idea  (i)  of  her  Majesty  herself ;  (2)  of  Royal  rank ;  (3)  of 
a  woman  ;  (4)  of  a  human  being;  (5)  of  likeness;  (6)  of 
chemical  action;  (7)  of  the  sun's  actinic  power;*  (8)  of 
the  effect  of  light  and  shade;  (9)  of  paper;  (10)  of  an 
inanimate  object;  (n)  of  substance;  and, finally,  (12)  of 
being  or  existence. 

Feelings,  again,  can  never  reflect  on  feelings,  but 
thoughts  often  reflect  on  thoughts.  The  vividness  of  a 
feeling  (deafening  sound  or  blinding  light)  may  destroy 
the  power  of  seme-perception  but  no  vividness  in  an  idea 
will  mar  intellectual  perception.  It  is  impossible  for  ideas 
to  be  too  clear  and  distinct.  Feelings  become  associated  t 
according  to  the  order  in  which  they  have  been  before 
felt,  but  ideas  may  become  associated  according  to  their 
intellectual  affinity. 

No  efforts  of  our  imagination,  moreover,  can  ever 
exceed  sensuous  experience.  We  can  never  imagine  what 
we  have  not  felt  in  itself  or  in  its  elements ;  but  it  is 
quite  otherwise  with  ideas.  We  have  the  idea  "  experi- 
ence," but  "experience"  was  never  felt;  and  it  is  the 
same  as  regards  an  act  of  seeing,  hearing,  or  of  any  other 
sense.  The  idea  of  " an  act  of  seeing"  is  one  thing,  but 
the  act  of  exercising  a  sensitive  power  is  quite  another. 
Nevertheless,  though  our  thought  can  thus  outrun  our 
sensible  experience  (the  experience  we  gain  through  our 
senses),  it  is  impossible  for  us  to  entertain  even  the  most 
abstract  thought,  except  by  the  help  of  some  mental  image 
of  things  sensibly  experienced — an  imagination  which 
serves  as  a  support  whereby  we  can  mentally  attain  things 
beyond  experience.  The  mental  images  which  generally 
serve  to  aid  us  in  our  highest  conceptions,  are  mental 
images  of  words  spoken  or  written. 

*  See  ante,  p.  in.  t  See  ante  p.  227. 

B 


258  ELEMENTS   OF   SCIENCE 

Our  knowledge  of  our  own  mental  and  bodily  activity, 
our  consciousness,  lies  at  the  foundation  of  our  whole 
intellectual  life,  as  the  parallel  affection  of  our  lower 
mental  nature  "consentience"*  is  at  the  foundation  of 
all  our  sense  perceptions.  That  we  are  conscious,  is  an 
ultimate  fact  of  our  being,  our  certain  knowledge  and 
perception  of  which  no  one  can  dispute.  In  so  far  as  it  is 
a  fact — a  state  or  quality  of  our  being — it  can,  like  other 
qualities,  be  mentally  abstracted,  and  "  consciousness"  is 
thus  both  a  fact  and  also  an  abstract  idea  gained  from 
our  own  perception  of  our  own  self-knowledge. 

Consciousness,  though  existing  at  each  instant,  is,  in  its 
very  essence,  continuous  and  conscious  of  its  own  persist- 
ence. We  each  of  us  know,  and  are  conscious,  not  only 
that  we  are  doing  whatever  we  may  be  doing  (as  the 
reader  is  conscious  that  he  is  reading  this  page),  but  also 
that  we  began  to  do  it  and  were  doing  something  else 
before  we  so  began.  The  supposition  that  consciousness 
could  be  composed  of  an  aggregate  of  different  "  states  "  of 
consciousness  is  an  absurdity.  Such  separate  "states," 
if  each  were  aware  only  of  itself,  could  not  constitute  that 
consciousness  which  we  know  ourselves  to  possess,  and 
which  is  aware  of  itself  as  continuous  and  successive. 
Consciousness  is  thus  a  persistent  intelligence  which,  as 
from  a  fixed  point,  reviews  the  procession  of  events,  and 
recognises  them  as  severally  belonging  either  to  the 
order  of  ideas,  or  to  what  it  recognises  as  real,  external 
existences. 

It  is  thus  manifest  that  we  have  a  certain  power 
of  directing  our  attention  upon  our  feelings,  or  our 
thoughts,  and  of  reflecting  on  them  and  comparing 
them,  as  well  as  of  voluntarily  attending  to  any  ex- 

*  See  ante,  pp.  227  and  252. 


MAN  259 

ternal  object — an  act  simulated  by  the  merely  sensitive 
activity  of  animals.* 

Conscious  reflection  and  attention  also  accompany  and 
serve  the  next  of  our  higher  mental  powers  to  which  we 
desire  to  direct  our  readers'  attention — namely,  intellectual 
memory.  To  this  the  merely  sensitive  memory  of  a 
beast  bears  a  certain  analogy,  which,  however,  is  very 
remote,  since  it  lacks  the  most  essential  character  of  the 
higher  faculty,  which  is  that  it  should  be  conscious. 
Evidently  we  cannot  be  said  to  "  remember "  anything 
unless  we  are  conscious  that  the  thing  we  so  remember 
has  been  present  to  our  mind  on  some  previous  occasion. 
An  image  might  recur  to  our  imagination  a  hundred 
times ;  but  if  at  each  recurrence  it  seemed  to  us  some- 
thing altogether  new  and  unconnected  with  the  past,  we 
could  not  be  said  to  remember  it.  It  would  rather  be 
an  example  of  extreme  forgetfulness. 

There  is  yet  a  further  distinction  between  sensuous 
and  intellectual  memory.  Every  now  and  then  we  direct 
our  attention  to  try  and  recollect  something  which  we 
know  we  have  for  the  moment  forgotten,  and  which  we 
instantly  recognise  when  we  have  managed  to  recall  it  to 
our  recollection.  But  besides  this  voluntary  memory,  we 
are  sometimes  startled  by  the  flashing  into  consciousness 
of  something  we  had  forgotten,  and  which  we  were  so  far 
from  trying  to  recollect,  that  we  were,  when  it  so  flashed 
into  consciousness,  thinking  of  something  entirely  differ- 
ent. Mental  movements  of  this  kind  maybe  distinguished, 
as  reminiscences,  from  those  which  follow  a  voluntary 
search  after  things  temporarily  forgotten,  which  are 
recollections.  It  is  obvious,  however,  that  neither  of  these 
kinds  of  memory  can  exist  without  consciousness.  Two 

*  See  ante,  p.  228. 


2<5o  ELEMENTS   OF   SCIENCE 

other  of  our  higher  faculties  are  our  two  powers  of  reason- 
ing or  inference.  One  of  these  is  commonly  termed  induc- 
tion, and  it  is  the  process  by  which  we  are  enabled  to  form 
judgments  more  or  less  probable,  or  even  certain.  Thus 
when  we  have  examined  many  kinds*  of  animals  belonging 
to  one  group,  e.g.,  the  group  of  opossums,  and  found 
that  they  all  possess  certain  peculiar  bones,  we  judge  that 
if  a  new  species  is  discovered  it  will  also  possess  such 
bones.  Such  a  judgment,  however,  can  rarely  be  an 
absolutely  certain  one.  But  we  may  be  certain  in  some 
cases.  Thus  by  the  study  of  many  kinds  of  rock,  we  may 
recognise  the  truth,  by  means  of  fossils  found  in  them, 
that  different  animals  have  inhabited  the  earth  at 
different  times.  A  farther  development  of  this  kind  of 
mental  activity  leads  to  a  process  which  is  most  fruitful 
in  promoting  scientific  progress — namely,  the  formation 
and  verification  of  hypotheses.  This  process  consists  of 
guesses,  based  on  a  certain  number  of  anterior  observa- 
tions, which  guesses  are  subsequently  tested  by  examining 
whether  certain  facts,  specially  selected  as  tests,  confirm 
such  guesses  or  not. 

The  other  process  of  reasoning  is  termed  deduction  or 
ratiocination,  and  will  be  considered  in  the  next  chapter 
wherein  we  shall  introduce  the  student  to  the  elements  of 
logic,  and  also  make  some  additional  remarks  about 
induction.* 

Amongst  our  many  perceptions,  one  supremely  im- 
portant one  is  our  perception  whether  or  not  anything 
is  true — our  perception  of  truth.  The  truth  of  every 
proposition  of  every  science  with  which  we  have  so  far 
been  concerned,  consists  in  its  conformity  with  fact. 
"  Truth "  is  a  conformity  of  thought  with  things,  and 

*  See  vost,  p.  309. 


MAN  261 

our  power  of  apprehending  such  conformity  is  at  the 
root  of  our  whole  intellectual  life.  The  mental  acts  by 
which  we  perceive  that  anything  is  certainly  "  true,"  or 
has  been  found  certain  (like  the  acts  by  which  we 
apprehend  our  own  existence,  or  the  existence  or 
qualities  of  the  objects  which  we  directly  perceive),  are 
called  intuitions.  As  they  essentially  pertain  to  our 
intellect,  they  are  also  called  "intellectual  intuitions." 

Another  of  our  perceptions  of  the  highest  practical 
importance  is  our  perception  whether  any  given  action 
is,  under  its  circumstances,  a  "  good  "  action  or  not — our 
perceptions  of  goodness. 

This  perceptive  faculty  of  ours  must  be  carefully 
distinguished  from  keen  feelings  of  sympathy,  of  shame, 
or  of  regret.  The  idea  of  "  goodness  "  is  quite  distinct 
from  the  ideas  of  "utility"  or  "pleasure,"  and  is  a 
perception  or  "  intuition  "  of  duty  as  concerns  ourselves 
or  others.  The  radical  distinctness  which  exists  between 
our  idea  "goodness,"  and  every  other  conception,  is 
easily  shown  by  an  example.  Let  us  suppose  that  any- 
one is  told  he  "  should  pay  his  tailor,"  and  the  truth  of 
the  saying  is  disputed  by  him,  the  only  possible  way  of 
trying  to  convince  him  as  to  his  duty  in  that  respect, 
would  be  to  call  his  attention  to  some  more  general 
moral  precept,  such  as  "  every  man  is  bound  to  pay  his 
debts."  If  this  again  were  disputed,  we  might  further 
urge  :  "A  man  is  bound  to  satisfy  obligations  he  has 
voluntarily  incurred,"  and  so  on.  In  every  step  we  take 
to  explain  why  a  duty  should  be  performed,  there  must 
always  be  a  further  and  more  elementary  declaration  of 
duty,  until  we  come  to  some  assertion  of  the  kind  the 
truth  of  which  is  admitted  as  self-evident.  This  proves 
conclusively  that  no  judgment  as  to  moral  obligation 
could  ever  be,  or  could  ever  have  been,  developed  from 


262  ELEMENTS   OF   SCIENCE 

mere  likings  or  dislikings,  or  from  pleasurable  or  pain- 
ful feelings  occasioned  by  the  good-will  or  hostility  of  our 
fellow  creatures. 

The  last  of  our  faculties  to  which,  in  this  elementary 
work,  it  seems  to  us  indispensable  to  call  attention, 
is  our  faculty  of  will.  Our  acts  of  will,  our  volitions, 
may  be  of  two  different  kinds.  They  may  either  be  ( i ) 
acts  in  which  we  simply  follow,  without  any  deliberate 
choice,  our  spontaneous  inclinations ;  or  (2)  acts  in  which, 
after  full  deliberation,  we  elect  to  follow  a  course 
opposed  to  that  towards  which  the  balance  of  the 
attractions  and  repulsions  acting  on  us  would  lead  us  to 
pursue.  The  common  sense  of  mankind  leads  them  to 
perceive  this  distinction,  for  when  a  man  has  lost  this 
power  of  voluntarily  "  choosing,"  he  is  said  to  be  not 
accountable.  The  conscience  of  every  reasonable  man 
assures  him  that  he  has,  at  least  occasionally,  a  power  of 
voluntarily  fixing  his  attention  upon  one  thing  rather 
than  another ;  and  that  he  can,  at  any  rate  sometimes, 
act  in  oppositon  to  a  strong  temptation  to  violate  duty. 
Our  reason  tells  us  that  men  are  right  in  declaring  that 
no  moral  blame  can  be  attached  to  actions  over  which  a 
man  has  no  choice  but  which  he  is  simply  compelled  to 
perform. 

Thus  over  and  above  those  powers  which  we  possess, 
in  common  with  the  higher  animals,  we  possess  self- 
consciousness  and  powers  of  intellectual  perception, 
memory  and  reflection,  of  forming  abstract  ideas  (such  as 
being,  substance,  cause,  activity,  passivity,  self,  not-self, 
difference  and  succession,  extension,  position,  shape,  size, 
number,  motion,  novelty,  dubiousness,  necessity,  agree- 
ment, disagreement,  &c),  and  of  making  abstract  judg- 
ments. We  also  possess  a  power  of  reasoning,  of 
apprehending  truth  and  goodness,  as  such,  and  of  ivitting 


MAN  263 

in  conformity  with,  or  in  opposition  to,  our  moral 
perceptions.  Further  we  possess  a  power  of  language 
entirely  different  from  that  of  any  other  animal,  as  will 
appear  at  the  end  of  this  chapter. 

As  we  are  unable  to  entertain  any  thought  without 
the  accompaniment  of  some  mental  image  or  phantasm 
(as  it  is  sometimes  called),  so  we  are  unable  to  com- 
municate our  thoughts  to  others  without  giving  them 
some  audible  or  visible  signs,  and  this  fact  makes 
language  absolutely  necessary  for  a  social  being  such 
as  man. 

But  man  differs  from  other  animals,  in  the  long  time 
he  takes  to  attain  the  power  of  self-preservation  and  to 
reach  maturity.  Long  absolutely  dependent  on  parental 
aid,  he  requires  the  society  of  his  fellow-creatures  in 
order  that  he  may  attain  anything  like  his  normal  intellec- 
tual development.  It  is  from  his  fellows  that  he  learns 
the  use  of  language,  without  the  possession  of  which  it  is 
impossible  to  make  any  considerable  advance  in  know- 
ledge.* 

In  the  present  chapter,  it  only  remains  for  us  to 
examine  briefly  what  appears  to  be  the  intellectual 
nature  of  the  lower  races  of  mankind  (with  a  view  to 
forming  a  judgment  as  to  whether  they  possess  the  same 
essential  powers  of  mind  as  those  which  we  ourselves 
enjoy)  and  to  consider  language. 

Mankind  at  the  present  moment,  consists  of  a  great 
diversity  of  tribes  and  races,  aggregated,  partly  into  larger 
natural  groups,  and  partly  into  political  aggregations — 
states  or  nations.  Each  tribe,  each  race,  each  group  of 
races,  and  each  state  or  nation,  has,  of  course,  its 
separate  history  and  its  greater  or  less  antiquity,  its 

*  £>ee  "The  Qrigin  of  Human  Reason,"  pp.  166-171, 


264  ELEMENTS  OF  SCIENCE 

customs,  sentiments,  ideas,  and  language.  But,  as  before 
said,  they  all  agree  in  possessing  a  closely  similar  bodily 
structure. 

All  existing  men  supplement  their  natural  bodily 
powers  by  the  use  of  tools  and  weapons.  The  weapons 
of  even  very  rude  savages  are  commonly  ornamented,  and 
art  in  a  rudimentary  form  may  be  said  to  be  universally 
diffused.  All  tribes  of  mankind,  without  exception, 
possess  the  faculty  of  rational  speech,  and  the  language 
of  gesture  is  very  similar  amongst  savage  tribes  all  over 
the  world.  A  great  deal  has  sometimes  been  made  of 
the  alleged  inability  of  some  savages  to  count  more  than 
five,  or  even  three.  The  asserted  facts  are  doubtful, 
but  anyhow  no  one  pretends  that  there  are  savages  who 
cannot  count  as  much  as  that.  But  to  really  count  at 
all  implies  the  possession  of  the  idea  of  number,  which 
is  a  highly  abstract  idea  in  itself  and  implies*  much 
else. 

For  the  idea  "  number "  implies  comparison,  with 
a  simultaneous  recognition  of  both  distinctness  and 
similarity,  although,  of  course,  it  is  not  necessary  that 
the  fact  of  possessing  such  apprehensions  should  be 
expressly  adverted  to.  No  two  things  could  be  known 
to  be  "two,"  unless  we  apprehended  that  they  had 
"  existence,"  and  that  while  they  were  numerically 
distinct,  they  agreed  in  possessing  a  certain  degree  of 
similarity — that  they  were  things  which  belong  to  the 
same  order. 

That  many  savages  are  frequent  or  habitual  liars  is  an 
assertion  which  has  been  often  made  by  travellers,  while 
individuals,  or  exceptioral  tribes,  have  sometimes  been 
praised  for  truthfulness.  There  can  be  no  question, 

.  *  See  k<  The  Origin  of  Human  Reason,"  pp.  81-91. 


MAN  265 

however,  but  that  all  men  understand  what  stratagems, 
deceits,  and  lying  are,  and  this  they  cannot  have,  with- 
out possessing  a  comprehension  of  "  truth." 

It  is  an  unquestionable  fact  that  different  groups  and 
sections  of  mankind  differ  as  to  their  estimate  of  the 
moral  character  of  certain  actions;  but  this  does  not 
prove  that  there  are  any  tribes  of  men  who  are  devoid  of 
all  moral  perceptions.  The  prevalence  in  any  tribe  of 
practices  which  shock  us,  does  not  prove  that  they  have 
no  apprehension  of  morality.  Men  are  not  necessarily 
devoid  of  it  because  they  draw  their  ethical  lines  in 
different  places  from  those  we  do.  The  most  horrible 
actions  (such,  e.g.,  as  the  deliberate  slaying  of  aged 
parents)  may  really  be  the  result  of  true  moral  judgments 
formed  under  peculiar  conditions.  It  is  said  to  be  done  by 
some  savages  in  obedience  to  the  wish  of  their  fathers  and 
mothers,  who  think  thereby  to  escape  further  suffering 
in  life,  and  to  procure  prolonged  happiness  after  death. 
Their  parricidal  children  reason  accurately  from  mistaken 
principles — they  make  mistakes  as  to  matters  of  fact. 
Men  certainly  do  not  always  agree,  even  in  England, 
about  the  application  of  moral  principles  :  what  they 
agree  about  is  that  there  are  moral  principles.  Thieving 
may  be,  here  and  there,  encouraged  and  advocated,  yet 
dishonesty  is  nowhere  erected  into  a  principle,  but  is 
reprobated  in  the  very  maxim  "  honour  amongst 
thieves."  Frightful  cruelty  towards  prisoners  was 
practised  by  the  North  American  Indians,  but  it  was 
towards  prisoners,  and  cruelty  was  never  advocated  as  an 
ideal  to  be  always  aimed  at,  so  that  remorse  of  conscience 
should  be  felt  by  any  man  who  happened  to  have  let 
slip  a  possible  opportunity  of  inflicting  torture. 

Men  have  often  thought  it  "  right "  to  do  things 
which  were  in  fact  unjust,  but  they  have  never  thought 


266  ELEMENTS   OF   SCIENCE 

that  actions  were  "right"  because  they  were  "  unjust," 
or  "  wrong"  because  they  were  "  just." 

One  of  the  clearest  of  all  ethical  judgments  is  that  as 
to  "  justice  "  and  "  injustice ;  "  and,  by  common  consent, 
the  native  Australians  are  admitted  to  be  at  about  the 
lowest  level  of  existing  social  development,  while  the 
Esquimaux  cannot  be  said  to  be  an  elevated  race.  But 
Australians  (at  least  some  tribes  of  them)  are  of  opinion 
that  crimes  may  be  compounded  for  by  voluntary  sub- 
mission to  punishment  to  be  inflicted  by  those  who  have 
been  injured.  A  criminal  will  thus  submit  himself  to 
the  ordeal  of  having  spears  thrown  at  him  or  thrust 
through  certain  parts,  such  as  the  calf  of  the  leg  or 
under  the  arm,  by  those  he  has  injured.  But  if  the 
punishment  exceeds  the,  extent  sanctioned  by  the  native 
code,  or  is  inflicted  in  a  wrong  place,  then  the  man  so 
offending  becomes  liable  to  punishment  in  turn. 

A  yet  stranger  example  of  the  existence  of  distinct 
moral  perception  amongst  very  rude  people  is  furnished 
us  by  the  Greenlanders.  Should  a  seal  escape  with  a 
hunter's  javelin  in  it,  and  be  killed  by  another  Green- 
lander  afterwards,  it  belongs  to  the  former.  But  if, 
after  the  seal  is  struck  with  the  harpoon  and  bladder, 
the  string  breaks,  the  hunter  loses  his  right.  If  a  man 
finds  a  seal  dead  with  a  harpoon  in  it,  he  keeps  the  seal 
but  returns  the  harpoon.  Any  man  who  finds  a  piece 
of  driftwood  can  appropriate  it  by  placing  a  stone  on  it, 
as  a  sign  that  some  one  has  taken  possession  of  it. 

The  inhabitants  of  Tierra  del  Fuego  are,  if  possible, 
more  wretched  savages  than  the  Australians.  Yet  even 
these  have  an  unmistakable  perception  that  to  waste 
human  food  is  wrong,  and  may  justly  incur  retribution 
from  a  higher  power.  Although  there  may  be  savages, 
as  there  may  be  Englishmen,  who  seem  devoid  of  moral 


MAN  267 

feelings  or  ideas,  there  is  no  evidence  of  the  absence  of 
moral  perceptions  in  any  tribe  of  human  beings.  A 
power  of  occasionally  distinguishing  an  element  of  right 
and  of  wrong  in  certain  actions  is  a  power  possessed  by 
all  normally  constituted  human  beings.  Even  the  worst 
men  can  recognise  such  a  character  in  acts  of  treachery 
done  to  them  by  their  own  special  associates. 

Man  also  seems  habitually  to  have  formed  some  judg- 
ments about  matters  commonly  called  "  religious."  That 
is  to  say,  all  races  of  men  have  the  idea  of  the  existence 
of  some  kind  of  personal  relation  between  themselves 
and  some  invisible  being  or  beings — malevolent  or  be- 
nevolent— with  more  than  human  power  and  possessing 
faculties  more  or  less  analogous  to  human  intelligence 
and  will.  The  relations  which  exist,  and  should  exist, 
between  human  beings  constitute  the  science  of  socio- 
logy. The  most  general  expression,  then,  for  natural 
religion  is,  a  code  regulating  the  relations  which  should 
exist  between  human  beings  and  invisible,  non-human 
intelligences.  It  is  a  sort  of  "  supernatural  sociology  ;  " 
it  merits  that  term  the  more,  inasmuch  as  some  regula- 
tions as  to  the  conduct  of  men  amongst  themselves 
generally  enter  into  it.  The  universal  tendency  of  even 
the  most  degraded  tribes  to  practices  which  clearly  show 
their  belief  in  preternatural  agencies  is  too  notorious  to 
admit  of  serious  discussion,  while  the  probably  all  but 
universal  practice  of  some  kind  of  funeral  ceremony 
speaks  plainly  of  as  widespread  a  notion  that  the  dead  in 
some  sense  yet  live.  Many  funeral  arrangements  are 
evidently  intended  to  impede,  or  render  impossible,  the 
return  of  the  deceased  to  the  home  he  has  left. 

It  is  not,  of  course,  meant  to  affirm  that  all  savage 
men,  any  more  than  all  civilised  men,  believe  in  a  future 
life,  or  in  one  or  many  gods;  but  nevertheless,  the 


268  ELEMENTS   OF  SCIENCE 

reality  or  probability  of  some  quasi-social  relations 
between  men  and  invisible  intelligences  is  a  common 
attribute  of  mankind. 

Considering  all  the  known  facts,  it  is,  in  our  judgment, 
certain  that  all  men  possess  an  intellectual,  as  well  as  a 
bodily,  nature  which  is  essentially  one,  however  either 
may  vary  in  minor  details.  As  has  been  said  by  an 
authority  in  these  matters  :  *  "  There  are  multitudes  of 
negroes  who  reach  as  high  an  intellectual  level  as  many 
Europeans.  Man's  craving  to  learn  the  causes  at  work 
in  each  event  he  witnesses,  the  reason  why  each  state  of 
things  he  surveys  is  such  as  it  is  and  no  other,  is  no 
product  of  high  civilisation,  but  is  a  characteristic  of  the 
human  race  down  to  its  lowest  stage.  Among  rude 
savages  it  is  still  an  intellectual  appetite,  the  satisfaction 
of  which  absorbs  many  a  moment  not  engaged  in  war, 
sport,  food,  or  sleep."  What  can  more  plainly  indicate 
the  presence  of  this  intellect  than  the  apprehension  of 
those  very  abstract  ideas  indicated  by  questions  as  to 
"  what,"  "  how,"  and  "  why."  The  investigation  of  such 
questions  constitutes,  as  we  shall  see,  the  highest  form  of 
science,  and  depends  upon  man's  power  apprehending 
the  ideas  "  causation  "  and  "  a  cause,"  ideas  which  are 
born  of  our  knowledge  of  our  own  powers  of  mental 
determination,  and  of  giving  effect  to  such  mental  deter- 
mination, by  our  external  acts,  as  also  by  the  resistances 
our  efforts  meet  with. 

The  study  of  man,  of  our  own  nature,  especially  as 
revealed  to  us  by  psychology  (that  is,  through  the  inter- 
rogation of  our  own  consciousness),  reveals  to  us  the  most 
wonderful  and  important  novelty  wherewith  our  elemen- 
tary study  of  the  universe  has  made  us  acquainted.  In 

*  Mr.  Tylor. 


MAN  269 

the  preceding  chapter  we  first  met  with  two  activities 
which  were  wonderfully  different  from  any  to  be  recog- 
nised as  existing  in  the  inorganic  world,  the  first  of  these 
was  life  and  the  possession  by  certain  beings  of  a  power 
of  internal  growth  ultimately  resulting  in  the  generation 
of  new  individuals.  The  second  wonder  was  that  faculty 
of  feeling,  which  seemed  to  be  bound  up  with  the 
possession  by  an  organism  of  a  certain  kind  of  tissue, 
so  that  only  a  section  of  the  whole  organic  world  could, 
with  certainty  be  deemed  to  possess  it.  But  the  higher 
animals,  we  saw,  have  such  complex  and  definite  sensitivity 
that  it  is  evident  they  not  only  possess  special  senses,  but 
can  sensuously  perceive  objects  about  them,  that  they 
possess  imaginations  and  a  kind  of  memory,  with  emotions 
and  anticipations  of  feelings  yet  to  be  experienced. 

In  the  present  chapter  we  make  an  advance  upon 
what  we  have  previously  studied,  which  is  far  greater 
than  the  advance  we  made  in  passing  from  the  non- 
living world  to  the  world  instinct  with  life  and  feeling. 
For  now  we  have  entered  upon  the  world  of  intellec- 
tuality— the  world  of  thought. 

And  here  we  put  aside  all  questions  of  origin  and 
essential  nature,  as  we  before  did  with  respect  to  life 
and  the  physical  forces.  When  treating  of  heat,  light, 
&c.,  we  declared  that  an  elementary  work  like  the 
present  was  not  the  place  wherein  to  consider  the 
problems  of  what  such  physical  forces  in  themselves 
might  be*,  and  in  describing  lifef  we  forbore  to  enter 
upon  the  question  what  life  is,  as  similarly  beyond  our 
present  aim.  So  as  regards  intellect  and  thought,  it 
matters  not  to  us,  here  and  now,  how  or  whence  they  came 
to  be,  how  early  in  life  they  may  show  themselves,  or  how 

*  See  ante,  p.  86.  t  See  ante,  p.  189. 


270  ELEMENTS   OF  SCIENCE 

universally  they  may  exist  amongst  our  fellow  men.  If 
only  we  know  that  we  ourselves  are  conscious  and  can 
reflect,  mentally  abstract,  and  judge,  and  know  that  we 
are  so  doing,  that  is  enough  to  make  us  absolutely  certain 
we  possess  a  power,  different  indeed  from  each  and  all  the 
powers  which  have  been  previously  spoken  of  in  this 
little  work.  Moreover,  this  knowledge  is  the  most 
absolutely  certain  of  all  knowledge.  However  we  may 
doubt,  we  cannot  doubt  that  we  think  while  we  are 
thinking,  whatever  may  be  the  object  of  our  thoughts. 
And  thought  is  our  ultimate  test  of  truth.  Even  in 
investigating  the  properties  of  material  bodies,  it  is  to 
thought  we  must  ultimately  appeal.  Only  by  that  can 
we  know  what  we  may  have  done,  and  it  is  that  which 
judges  between  conflicting  indications  of  different  sense- 
impressions.  Our  senses  are  truly  tests  of  certainty,  but 
not  the  test.  Self-conscious,  reflective  thought  is  and 
must  be  our  last  and  ultimate  criterion. 

And  now  let  the  reader  consider  what  his  own  intel- 
lect tells  him  about  its  own  powers  and  activities  as 
revealed  to  him  directly  in  his  consciousness.  He  will 
recognise  that  his  intellect  (that  is,  he  himself)  exists 
continuously,  so  that  he  knows  that  it  is  that  same  in- 
tellect of  his  which  both  began  to  think  of  this  question, 
and  now  still  continues  to  think  about  it.  He  will 
also  recognise  that  he  knows  objects  and  persons  about 
him,  and  what  is  happening  to  them  before  his  eyes,  while 
he  all  the  time  remains  something  distinct  from  them. 
He  can  reflect  over  the  different  things  he  remembers  to 
have  thought  of  during  the  morning,  and  recognise  that 
they  have  constituted  a  series  of  thoughts.  He  can  thus 
think  of  them  as  a  whole — a  series — or  he  can  select  one 
of  his  thoughts,  or  a  group  of  them,  for  reconsideration. 
He  knows  also  what  he  is  about,  what  he  is  doing,  or 


MAN  271 

what  may  be  being  done  to  him.  As  to  external  objects 
and  events,  he  can  compare  them  and  see  some  of  the 
relations  in  which  they  may  stand  to  one  another, 
following  up  different  lines  of  thought  as  he  will. 

But  such  a  power  as  this  intellect  of  his,  aware  of  all 
these  things  and  mentally  present  to  them  all,  cannot  be 
made  up  of  parts,  but  must  be  the  most  perfect  and 
simple  unity  we  can  conceive  of.  It  cannot  therefore  be 
either  a  material  substance  or  a  physical  force,  and  still 
less  any  combination  of  such  substances  and  forces,  to 
which  it  presents  the  greatest  contrast.  Nevertheless 
we  each  of  us  have  also  the  structure,  the  faculties  and 
the  feelings  of  a  sort  of  ape.  Therefore  each  of  us  is  a 
unity  with  two  sets  of  faculties;  (i)  one  essentially 
sensuous  and  material,  the  source  of  all  bodily  functions 
and  animal  feelings;  the  other  (2)  essentially  intellectual 
and  immaterial,  which  can  examine  and  judge  the  world 
about  it  and  also  its  own  activities. 

LANGUAGE. — Next  we  must  consider  that  most  funda- 
mental and  distinctive  character  of  man  as  an  intellectual 
being — namely,  his  power  of  speech  and  of  making  known 
his  meaning  by  intellectual  gestures. 

We  have  noted*  how  the  higher  animals  by  vocal  cries 
and  bodily  movements,  or  gestures,  can  give  expression 
to  the  various  different  feelings  by  which  they  are  ani- 
mated; as  also  that  human  language  is  something  entirely 
different!  therefrom.  The  time  has  now  arrived  for  paying 
direct  attention  to  this  very  important  subject.  That  it  is 
very  important  is  manifest,  for  it  is  impossible  for  us  to 
make  known  our  thoughts  to  others,  save  by  the  help  of 
bodily  signs,  vocal  or  other.  But  it  is  more  important 

*  See  ante,  p  1229.  t  See  ante,  p.  263. 


272  ELEMENTS   OF   SCIENCE 

still,  for,  as  before  said,*  we  cannot  even  think  without 
some  imagination  of  things  noted  by  the  senses,  and 
especially  of  words,  as  spoken,  heard  or  read,  or  of 
gestures  as  seen  in  reality,  or  in  pictures,  or  as  felt. 
We  almost  always  think  in  words,  though  we  may 
think  by  the  aid  of  objects  or  actions  pictured  by 
the  imagination. 

We  have  to  consider  language,  in  the  ordinary  sense  of 
that  term,  as  a  medium  for  expressing  ideas  and  inten- 
tions, asking  questions,  stating  facts,  and  carrying  on 
conversation.  Since  then  by  "  language  "  we  ordinarily 
mean  spoken  articulate  sounds,  serving  for  intellectual 
intercourse,  we  will  begin  by  examining  some  very 
simple  expressions  of  the  kind.  Let  us  suppose  two 
men  to  be  standing  under  an  oak  tree,  and  that  this 
tree  begins  suddenly  to  show  signs  of  falling,  they  will 
fly  from  the  danger,  and  they  may  utter  cries  of  alarm, 
and  by  their  cries  and  gestures  they  may  give  rise  to 
sympathetic  feelings  of  alarm  in  persons  who  happen  to 
be  near  the  spot.  In  so  far  as  they  do  no  more  than 
this,  their  language  (whether  vocal  or  of  gesture)  is  but 
of  the  same  kind  as  the  language  of  emotion  in  the 
lower  animals. 

They  may,  however,  cry  out  "  That  oak  is  falling," 
that  is,  they  may  give  utterance  to  intellectual  language ; 
for  those  four  words  express  and  embody  much  more 
than  any  mere  feelings  or  emotions.  They  express  and 
signify  abstract  ideas. 

(1)  The  word  oak  is  a  conventional  sign  for  the  idea, 
or  conception,  of  that  kind  of  tree,  and  is  an  abstract 
term  applicable  to  every  actual  or  possible  oak. 

(2)  The  word  that  is  one  which  serves  to  separate  off, 

*  See  ante,  p.  257. 


MAN  273 

in  the  mind,  the  one  particular  falling  oak  from  all 
others.  It  implies  the  idea  of  a  unity  of  a  different  sort 
from  the  unity  implied  by  the  word  "  oak." 

(3)  The  word  is   denotes  the    most    abstract   of   all 
abstract    terms,  the  idea  of    "  existence "   or  "  being," 
the  significance  of  which  has  been  before  pointed  out.* 

(4)  The    word  falling   is  a    term    denoting    another 
abstraction — the  conception  of  a  "  quality  "  or  "  state." 
The  idea  is  one  which  is  evidently  capable  of  a  very  wide 
application,  namely,  to  everything  which  may  fall.     Yet 
the  idea  itself  is  one  single  idea. 

A  word  by  itself  has  but  a  very  imperfect  significa- 
tion. It  needs  the  addition,  expressed  or  implied,  of 
others  to  give  it  full  meaning — to  explicitly  f  express  a 
judgment.  Such  a  congeries  of  words  is  a  sentence,  and 
the  four  words  "  That  oak  is  falling,"  is  one  such  sig- 
nificant set  of  words. 

What  is  true  of  this  single  sentence  is  true  of  all  sen- 
tences. All  human  language  (apart  from  mere  emotional 
manifestations)  necessarily  implies  and  gives  expression 
to  a  number  of  abstract  ideas.  It  is  impossible  for  even 
the  most  brutal  savage  to  speak  the  simplest  sentence 
without  having  first  formed  for  himself  highly  abstract 
ideas.  Wherever,  therefore,  language  exists,  there  also 
must  exist  the  power  and  the  active  exercise  of  mental 
abstraction. 

All  our  words  express  abstract  ideas,  except  proper 
names,  and  words  denoting  individuals,  such  as  the 
words  "I"  "thou"  "they,"  &c.  Words  which  denote 
individual  objects,  real  or  ideal,  are  termed,  as  we  all 
know,  "  substantives,"  as  a  parrot,  a  desire.  A  word 
which  indicates  that  anything  acts  or  is  acted  on,  is,  as 

*  See  ante,  p.  253.  t  See  ante,  p.  255. 

S 


274  ELEMENTS   OF  SCIENCE 

the  reader  is,  of  course,  well  aware,  called  a  "  verb,"  as, 
the  parrot  screams,  or,  he  shot  the  parrot.  Of  course 
nothing  can  act  or  be  acted  on,  unless  it  exists,  but  there 
is  a  special  verb,  called  the  substantive  verb,  which 
expresses  existence.  It  is  the  verb  to  be,  and,  in  its 
form  "  is,"  it  asserts  what  has  above  been  pointed  out. 
When  it  asserts  a  relation  between  one  thing  and  another, 
it  is  spoken  of  as  the  copula.  Thus  in  the  sentences, 
"  That  man  is  a  father,"  "  The  sky  is  blue,"  and  "  That 
oak  is  falling,"  the  term  "  is  "  merits  that  appellation. 

Terms  which  denote  qualities  or  states  of  objects  are 
"  adjectives,"  or  verbs  in  that  form  which  is  called  a 
"  participle  " — as  in  the  last  two  sentences  given  as 
examples,  namely,  "  The  sky  is  blue"  and  "  That  oak  is 
falling:3 

Elementary  as  this  work  is  intended  to  be,  it  is  not 
our  object  to  teach  in  it  such  things  as  orthography  or 
grammar,  we  will  therefore  pass  on  to  further  point  out 
wherein  the  essentials  of  human  language  consist. 

The  faculty  of  abstraction  must,  as  before  said,  be 
possessed  by  every  one  who  speaks.  But  that  faculty  is 
also  possessed  by  men  who  do  not  speak.  Various 
kinds  and  degrees  of  dumbness  may  arise  from  different 
forms  of  defective  memory  as  to  words,  due  to  different 
physical  defects  of  brain- structure,  such  defects  im- 
pairing those  powers  of  feeling  and  imagination,  on  the 
integrity  of  which  the  exercise  of  our  intellectual 
faculties  depends.  The  absence  of  words  does  not 
necessarily  imply  the  absence  of  ideas.  Very  wonderful 
are  the  gestures  of  deaf-mutes*  which  make  it  un- 
questionable that  human  beings  may  possess  distinct 
intellectual  conceptions  in  the  entire  absence  of  spoken 

*  See  "The  Origin  of  Human  Reason,"  pp.  138-171. 


MAN  275 

words.  Abstract  ideas,  then,  can  exist  without  such 
words,  but  there  is  no  evidence  that  they  can  continue 
to  exist  without  some  embodiment,  some  form  of  lan- 
guage, some  corporeal  expression,  either  by  voice  or  by 
gesture.  Language  therefore  is  a  consequence  of 
thought,  and  abstract  ideas  are  indispensable  pre- 
liminaries to  language.  We  see  this  in  our  common 
experience.  When  in  the  cultivation  of  any  science  or 
art,  newly  observed  facts,  or  newly  devised  processes, 
give  rise  to  new  conceptions,  new  terms  are  invented  to 
give  expression  to  such  conceptions.  Thus  new  words 
arise  as  a  consequent  *  and  not  as  an  antecedent,  of  such 
intellectual  actions.  New  terms  are  always  fitted  to 
fresh  ideas,  and  not  fresh  ideas  to  new  terms.  That 
language  is  dependent  on  thought,  not  thought  on 
language,  is  demonstrated  for  us  by  the  lightning-like 
rapidity — a  rapidity  far  too  great  for  words — with 
which  our  minds  may  detect  a  fallacy  in  an  argument. 
This  instantaneousness  is  not  the  mere  mental  ejacula- 
tion of  the  word  "  no,"  but  is  due  to  our  having  appre- 
hended the  relations  existing  between  different  portions 
of  the  argument.  The  most  rapid  cry  or  gesture  of 
negation,  is  often  the  sign  of  intellectual  perceptions 
which  would  require  more  than  one  sentence  fully  to 
express,  but  which  are  perceived  too  rapidly  for  even  the 
mental  repetition  of  the  words  of  such  sentences. 
Nevertheless,  these  intellectual  perceptions  show  them- 
selves by  bodily  signs — sounds  or  gestures — and  even  all 
our  silent  thought  is  carried  on  by  the  aid  of  some 
imagined  bodily  signs,  without  which,  as  we  before 
observed,  we  cannot  think.  Human  language  seems 


*  See  a  correspondence  with  Professor  Max-Muller,  cited  in 
"  Origin  of  Human  Reason,"  pp.  99-117. 


276  ELEMENTS   OF   SCIENCE 

quite  unable  to  grow,  or  even  to  endure,  without  some 
embodiment,  without  corporeal  expressions  of  some  kind. 
Thus  language  of  word  or  gesture  is  the  necessary  means 
of  human  thought  as  well  as  its  necessary  consequence. 

The  mental  and  bodily  sides  of  language  are  so  in- 
timately united  that,  though  the  mental  side  is  anterior, 
it  at  once  seeks,  as  it  were,  to  incarnate  itself,  and, 
under  normal  circumstances,  does  incarnate  itself,  in 
corporeal  expression.  Deaf  mutes  will  spontaneously 
evolve  a  gesture  language  through  which  they  can 
understand  each  other  and  communicate  their  ideas. 
Rational  conceptions,  therefore,  can  evidently  exist 
without  words,  but  rational  words  cannot  exist  without 
conceptions  or  abstract  ideas.  But  though  a  language 
of  gesture  may  be  elaborated,  and  even  carried  to  much 
perfection,  as  we  see  in  certain  ballets,  yet  spoken  lan- 
guage is  so  enormously  superior  to  that  of  gesture  that 
no  comparison  can  be  made  between  the  two  vehicles  for 
the  expression  of  human  thought. 

The  intellect  is  the  common  root  from  which  both 
thought  and  language  (whether  of  speech  or  gesture) 
spring,  and  thenceforth  continue  and  develop  in 
unseparable  union. 

Language,  then,  is  of  two  radically  distinct  kinds 
— (i)  the  language  of  feeling  which  we  possess  in 
common  with  animals;  and  (2)  the  language  of  the 
intellect  which  is  absolutely  peculiar  to  man. 

There  are  also  various  subdivisions  of  each  of  these 
two  kinds  of  language. 

Of  the  mere  language  of  the  emotions  and  of  feeling 
we  may  have : 

(i)  Sounds  which  are  neither  articulate  nor  rational, 
such  as  cries  of  pain  or  the  murmur  of  a  mother  to  her 
infant. 


MAN  277 

(2)  Sounds   which   are    articulate   but  not   rational, 
such  as  many  oaths  and  exclamations,  and  the  words  of 
certain  idiots,  who  will  repeat,  without  comprehending, 
every  phrase  they  hear.     This  habit  is  parallel  to  that 
power  of  irrationally  emitting  articulate  sounds   which 
some  birds  possess. 

(3)  Gestures  which    do   not   answer  to  rational   con- 
ceptions, but  are  the  bodily  signs  of  pain  or  pleasure,  of 
passion  or  emotion. 

The  subdivisions  of  the  language  of  the  intellect  are : 

(1)  Sounds   which   are    rational   but   not  articulate, 
such   as   inarticulate   ejaculations   by  which   we   some- 
times  express   assent  to,   or   dissent  from,  given   pro- 
positions. 

(2)  Sounds   which   are  both  rational   and  articulate, 
constituting  true  "  speech." 

(3)  Gestures  which  give   expression   to   rational  con- 
ceptions, and  are  therefore  corporeal,  but  not  "  oral," 
manifestations    of    abstract    thought.     Such  are   many 
of  the  gestures  of  deaf-mutes,  who,  being  incapable  of 
articulating  words,  have   invented   or   acquired  a  true 
gesture-language. 

(4)  A  peculiar  modification   of    gesture  which  takes 
the  shape  of  (a)  pictorial  signs  of  objects  or  actions ;  or 
(b)  signs  of  sounds  which,  taken   together,  form  words 
signifying   abstract  ideas — (i.)  picture ;  or  (ii.)  written 
language. 

Thus  the  essence  of  true,  or  intellectual,  language  is 
mental,  and  is  a  form  of  intellectual  activity  which,  as 
the  mental  constituent  of  speech,  may  be  distinguished 
as  the  "  mental  word  "  or  verbum  mentale.  The  other 
element  of  speech,  that  which  gives  it  external  ex- 
pression, may,  on  the  other  hand,  be  distingushed  as  the 
"  spoken  word  "  or  verbum  oris.  The  latter  ever  follows 


278  ELEMENTS   OF  SCIENCE 

the  former,  as  is  evident  from  that  process  which 
goes  on  in  every  science  as  it  progresses,  the  process 
of  inventing  (as  before  said)  fresh  terms  in  order 
to  denote  new  or  more  complete  and  better  defined 
conceptions. 

The  mental  word  is  normally  in  excess  of  the  spoken 
word,  as  is  shown  by  our  use  of  metaphors.  Had  not 
the  intellect  the  power  of  apprehending,  through  the 
senses,  what  is  beyond  the  power  of  feeling,  metaphor 
would  not  exist.  It  exists  because  speech  is  too  narrow 
for  thought,  and  because  words  are  often  too  few  to 
convey  the  ideas  of  the  mind. 

The  mental  word  is  also  so  rapid,  it  often 
happens  that  speech  cannot  keep  pace  with  it.  That 
such  is  the  case  as  regards  writing  most  readers  have 
probably  already  noted. 

But  there  is  the  closest  connection  between  the 
mental  and  the  spoken  word,  which  ordinarily  ac- 
company each  other  most  closely,  as  the  concavities 
and  convexities  of  the  opposite  sides  of  an  undulating 
line.  They  are  nevertheless  sometimes  abnormally 
separated  through  some  physical  defect,  the  tongue 
repeating  other  words  than  those  the  mind  desires  to 
give  expression  to.  A  paralysed  man  may  possess  the 
mental  word  though  hindered  from  manifesting  it 
externally  by  spoken  words,  or  even  by  gestures.  But 
normally,  as  just  observed,  the  external  and  internal 
powers  are  inseparable.  When  the  intellectual 
activity  exists,  it  seeks  external  expressions  of 
symbols — verbal,  manual,  or  what  not — by  the  voice 
or  by  gesture-language.  Some  form  of  symbolic 
expression  is,  therefore,  the  necessary  consequence  in 
man  of  the  possession  of  reason,  while  it  is  impossible 
that  true  speech  can  for  a  moment  exist  without  the 


MAN  279 

co-existence  with  it  of  that  intellectual  activity  of  which 
it  is  the  outward  expression. 

But  language  reacts  upon  the  mind  of  him  who  uses 
it.  Besides  being  an  interpreter  of  thought,  it  exercises 
a  powerful  influence  on  the  process  of  thinking,  (i)  It 
helps  us  to  analyse  new  complex  impressions  by  the 
distinctness  and  definiteness  which  it  has  given  to  our 
conceptions  of  previous  impressions.  (2)  By  memory 
or  writing  it  enables  us  to  preserve  the  results  of 
mental  activity  for  future  service.  (3)  It  greatly  aids 
mental  processes  by  substituting  a  short  word  for  a  very 
complex  idea  accompanied  by  a  variety  of  mental 
images.  Signs,  when  their  meaning  is  definitely 
established,  can  be  used  as  counters,  and  we  can 
temporarily  neglect  what  they  signify  while  we  are 
working  with  them  till  we  come  to  a  final  result,  as  in 
the  case  of  arithmetical  and  algebraic  signs,  as  we 
saw  in  the  second  chapter.*  (4)  Finally  language 
serves,  as  every  one  knows,  as  a  means  of  communica- 
tion, and  so  has  become  an  enormous  factor  in  mental 
development,  since,  as  we  have  seen,  the  mental 
development  of  each  man  depends  directly  on  his 
intellectual  environment  which  appears  absolutely 
indispensable  to  it,  although  neglected  children  and 
deaf  mutes  are  saidf  to  be  able  to  form  a  sort  of 
language  for  themselves. 

Just  as  all  races  of  men  are  men,  and  exhibit  no  great 
or  essential  structural  or  functional  differences,  so  they 
all  possess  the  power  of  speech,  although  that  power  is 
expressed  in  many  different  languages,  each  of  which  has 
its  own  method  of  expression.  In  Latin  one  word,  amavi, 


*  See  ante,  pp.  12  and  23. 

t  See  "  Origin  of  Human  Reason,"  p.  232. 


280  ELEMENTS   OF   SCIENCE 

serves  to  express  what  in  English  requires  the  three 
words  "  I  have  loved." 

How  the  various  sounds  which  in  different  languages 
express  different  ideas  are  agglutinated,  isolated,  and 
changed  in  form  or  "  inflected,"  is  a  matter  which  cannot 
be  gone  into  here.  For  such  further  information  the 
reader  is  referred  to  the  various  works  on  the  science  of 
language,  or  Philology. 

But  objections  to  the  essential  unity  of  language  have 
been  made  because  certain  differences  exist  in  the  mode 
of  giving  expression  to  the  same  ideas.  Thus,  it  has  been 
affirmed  that  some  languages  are  defective  as  regards 
the  substantive  verb,  and  that  therefore  those  who  speak 
it  have  not  the  idea  of  existence.  But  if  there  are  tribes 
of  men  who  cannot  say,  "  He  is  sitting,"  "  She  is  stand- 
ing," "  It  is  falling/'  it  is  quite  enough  if  they  can  say, 
"  He  sits,"  or  "  Stands  she  "  or  "  It  falls."  Such  expres- 
sions show  that  they  have  the  idea.  It  is  a  man's  mean- 
ing, and  his  power  of  making  that  meaning  evident,  which 
is  alone  important,  the  system  of  signs  by  which  he 
expresses  it  is  a  relatively  trivial  matter. 

It  is  not  a  multitude  of  words  which  constitutes  the 
perfection  of  language.  Some  exceptionally  endowed 
minds  can,  with  a  few  pregnant  words,  bring  to  the 
minds  of  others,  perceptions  which  could  be  conveyed 
by  inferior  natures  only  by  means  of  long  and  laboured 
discourses.  Therefore,  the  minimum  of  language  which 
can  co-exist  with  the  due  expression  of  thought  is  the 
best. 

The    ultimate    facts    as    to  language   may   be  thus 


(i)  Thought  is  the  root  of  every  sort  of  intellectual 
language,  and  is  anterior  to  outward  expression  of  what- 
ever kind. 


MAN  281 

(2)  Language  is  the  external  expression  of  the  verbum 
mentale. 

(3)  The  simplest  elements  of  thought  being,   as   we 
have  seen,*  an  "  implicit  judgment"  or  "concept,"  the 
simplest   element   of   language   must    be    the    external 
expression  of  an  implicit  judgment — i.e.,  a  word  or  term. 

(4)  The  most  elementary  complete  act  of  the  mind 
being  a  judgment,*  the  most  elementary  complete  ex- 
pression in  language  must  be  a  judgment  expressed  in 
words  or  other  signs — i.e.,  an  enunciation  or  proposition. 

This  brief  sketch  of  the  most  important  character- 
istics of  man,  as  distinguished  from  other  animals,  must 
suffice  as  an  introduction  to  the  elements  of  the  science 
of  human  nature,  or  Anthropology.  Without  such  ele- 
mentary knowledge  as  we  have  here  attempted  to  convey, 
any  study  of  nature,  including  man,  must  be  futile  and 
deceptive.  Having  now  indicated  what  are  the  essential 
characters  of  the  human  intellect,  we  must  devote  the 
following  chapter  to  an  exposition  of  the  main  laws 
which  govern  the  employment  of  our  wonderful  faculty 
of  reason. 

*  See  ante,  p.  255. 


CHAPTER    VIII 
LOGIC 

LOGIC  is  the  science  which  treats  of  the  laws  that  regu- 
late human  thought.  It  is  the  science  which  elucidates 
the  mode  in  which  thought  must  be  carried  on  in  order 
that  we  should  arrive  at  truth.  Nevertheless  it  does  not 
concern  itself  with  the  truth  of  the  thoughts  themselves 
— their  conformity  with  external  things — but  only  with 
the  mode  in  which  thought  must  be  employed  in  order 
to  attain  two  ends.  The  first  of  these  (a)  is  the 
avoidance  of  certain  errors  which  would  necessarily 
arise  were  the  rules  of  logic  violated.  The  second  (b) 
is  the  manifestation  of  truths  which  are  involved  in, 
and  depend  upon,  the  recognition  of  other  antecedent 
truths,  from  the  truth  of  which  they  necessarily  follow 
as  consequences. 

The  importance  of  logic  as  a  key  to  all  reasoning,  and 
therefore  to  a  large  part  of  every  science,  is  enormous. 
On  this  account,  though  we  must  refer  our  readers  to 
special  treatises  for  all  but  the  elements  of  it,  we  propose 
to  treat  these  logical  elements  at  some  little  length. 

The  first  meaning,  the  first  intention,  we  have  in 
thinking  about,  or  naming  anything,  relates  directly  to 
whatever  we  so  think  about  or  name.  Thus,  for  example, 
if  we  think  (i)  "a  horse,"  or  (2)  "that  horse  is  lame," 
or  (3)  "its  lameness  shows  that  the  man  who  sold  it 
cheated,"  in  each  of  these  cases  our  meaning  or  "in- 


LOGIC  283 

tention  "  respectively  is  (i)  the  kind  of  animal  we  have 
formed  a  concept  of;  (2)  the  lameness  we  judge  about;  or 
(3)  the  dishonest  action  we  infer  to  have  taken  place. 
But  these  three  thoughts  have  also  the  quality  of  being 
thoughts  of  a  special  kind — belonging  to  one  or  other 
sets,  or  kinds,  or  groups,  or  forms  of  thought.  Moreover, 
each  of  them  belongs  to  a  different  group  or  form — 
they  are  different  "  forms"  of  thought.  Thus  the  first 
(i)  is  a  concept,*  the  second  (2)  is  a  judgment,*  and  the 
last  (3)  is  an  inference — a  conclusion  arrived  at  by  a 
process  of  reasoning. 

Thus  each  thought  signifies,  not  only  what  is  our 
meaning,  or  first  intention  in  using  it,  but  also, 
what  "  order  "  of  thought  it  is.  This  latter  signification 
is  said  to  be  the  second  meaning  or  second  "  intention  " 
of  each  thought.  Therefore  logic  is  called  the  science  of 
second  intentions.  By  this  it  is  meant  that  logic  treats 
of  the  forms  of  thought,  regardless  of  the  matter  to 
which  such  thought  may  refer.  Thus,  e.g.,  in  the  thought 
"that  horse  is  lame,"  the  form  of  the  thought  is  a 
"judgment."  The  matter  of  the  thought  is  the  fact  of  lame- 
ness, with  which  fact  logic  has  nothing  whatever  to  do. 
As  therefore  it  has  only  to  do  with  the  forms  which 
thought  may  assume,  it  is  justly  called  "  the  science  of 
the  formal  law  of  thought." 

But  though  logic  has  nothing  to  do  with  the  material 
truth  of  thoughts,  it  has  to  do,  as  before  said,  with  so 
conducting  processess  of  thought  as  to  secure  that  they 
shall  not  themselves  be  the  occasion  of  error,  but,  on  the 
contrary,  aid  in  making  explicit,  truths  which  such 
thoughts  may  implicitly  contain.  Logic,  therefore, 
as  a  guide  to  just  and  valid  reasoning,  is  practical,  and 


*  See  ante,  p.  255. 


284  ELEMENTS   OF   SCIENCE 

consequently  is  an  art  as  well  as  a  science — it  is  the  art 
of  correct  thinking  and  of  valid  inference. 

The  science  of  logic,  as  "  the  science  of  the  forms  of 
thought,"  is  divisible  into  three  parts,  each  of  which 
deals  with  one  class  of  such  forms.  The  first  part  deals 
with  conceptions,  the  second  with  judgments,  and  the 
third  with  reasoning. 

The  first  part  which  thus  deals  with  "  conceptions,"  is 
also  said  to  be  occupied  about  names,  or  terms.  This 
is  said  on  account  of  the  intimate  association  which 
exists  between  each  thought,  or  verbum  mentale,  and  the 
word  which  signifies  it,  or  verbum  oris.*  The  connection 
is  so  close  that  we  may  henceforth,  in  this  chapter,  deal 
with  the  spoken  and  written  signs  of  thoughts  as  if  they 
were  the  very  thoughts  themselves ;  although  it  should 
nevertheless  be  remembered  that  we  are  not  treating  of 
names  as  such,  but  as  symbols  of  the  thoughts  they 
represent. 

A  "name,"  or  "term,"  is  a  human,  conventional  articu- 
late sound,  used  with  an  intention  of  signifying  something. 
There  are  various  kinds  of  names.  They  may  be  (T) 
universal — applicable  to  each  and  all  of  a  class  of  objects, 
e.g.,  "man,"  "true,"  &c. ;  (2)  collective — applicable  to  a 
whole  but  not  to  its  component  members,  e.g.,  "  army"; 
(3)  particular — applicable  to  but  a  portion  of  some  whole, 
e.g.,  "  some  Indians  " ;  (4)  singular — applicable  to  one 
only,  e.g.,  "  Julius  Caesar "  ;  (5)  universal — having  the 
same  signification  when  applied  to  different  objects,  e.g., 
"green,"  as  applied  to  foliage  and  a  lady's  dress;  (6) 
equivocal — one  sound  having  more  than  one  signification, 
e.g.,  "box";  (7)  analogous — when  one  signification 
applies  in  an  unequal  degree  to  different  objects.  Such 


*  See  ante,  p.  277. 


LOGIC  285 

analogy  may  be  (a)  one  of  proportion,  or  (b)  one  of 
attribution.  In  the  former  case  there  is  a  certain  agree- 
ment in  the  effects  produced  by  quite  dissimilar  causes, 
e.g.,  "the  staff  of  life,"  the  " foot  of  a  mountain," 
the  "  head  of  an  army,"  or,  as  we  may  say  of  a  vessel, 
"she  walks  the  waters  like  a  thing  of  life."  Words 
which  have  an  analogy  of  attribution  are  such  as  denote 
a  quality  which  primarily  and  properly  belongs  to  one 
object  but  is  attributed  to  another  as  bearing  some 
relation  (as  of  cause  or  effect)  thereto,  e.g.,  healthy  man, 
healthy  exercise,  healthy  appetite,  healthy  climate;  (8) 
abstract  * — denoting  some  form  or  quality,  considered 
apart  from  whatever  object  or  objects  it  may  pertain  to, 
e.g.,  "whiteness,"  "existence,"  "extension,"  &c. ;  (9) 
concrete — applicable  only  to  things  actually  existing,  or 
having  existed,  e.g.,  "  Descartes,"  "  these  sheep,"  &c. ; 
(10)  absolute — that  is,  a  name  the  signification  of  which 
refers  only  to  the  object  named,  e.g.,  "justice,"  "gold," 
&c. ;  (n)  connotative — that  is,  necessarily  implying  some- 
thing else,  e.g.,  "  white,"  "rapid,"  "  pianist,"  "son,"  &c. 
Terms  which  have  a  natural  relation  to  one  another,  such 
as,  e.g.,  father  and  son,  are  spoken  of  as  correlative.  (12) 
positive,  e.g.,'"''  strong;"  (13)  negative,  e.g.,  " insentient," 
as  applied  to  a  stone;  (14)  privative,  e.g.,  "insentient," 
as  applied  to  a  man  who  has  lost  the  power  of 
sensation;  (15)  transcendental — names  denoting  ideas 
of  attributes  which  are  incapable  of  (or  transcend)  classifi- 
cation, because  they  are  present  in  all  cases  and  pertain  to 
everything  which  there  is  to  classify,  e.g.,  "  existence." 

Universals  are  words  denoting  classes  of  things, 
or  attributes,  or  qualities,  which  may  exist  in  many 
things.  They  relate  to  things  as  they  exist,  apart  from 

*  See  ante,  p.  256. 


286  ELEMENTS   OF  SCIENCE 

all  apprehension  of  them.     A  horse,  and  our  idea  of, 
and  name  for,  a  horse,  remain  the  same,  whatever  may 
be  the  direction  of  our  mind  in  considering  such  things, 
and  the  same  is  the  case  with  regard  to  the  quality 
"  quadrupedal."     As  we  have  seen,*  living  things  are 
arranged  by  science  in  a  definite  classification.     Therein 
the  creatures  which  constitute  a  genus  are  always  the 
same,  and  the  terms  "genus"  and  "species"  can  never 
change  places.    But  there  are,  in  logic,  certain  things  and 
names,  which,  instead  of  being  constant,  change  accord- 
ing to  the  direction  in  which  the  mind  is  turned  as  it 
regards  them,  and  their  mode  of  classification  changes 
correspondingly,  and  in  this  way  classificatory  groups 
may  change  in  position  and  value.     Thus  we  may  think 
of  "  Jews,"  as  a  group.     Then  "  Jews  of  Middlesex," 
"  those  of  Essex,"  &c.  &c.,  will  be  minor  groups  subordi- 
nate to  the  larger  and  dominant  one  "Jews."     But  we 
may  also  first  think  of  "  Jews  of  Middlesex,"  and  then 
of  those  which  are  "  reformed,"  and  those  which  are 
"  unreformed,"  which  will  then  constitute  subordinate 
groups,  while  the  group  "  Jews  of  Middlesex  "  will  change 
from  being,  as  before,  subordinate,  and  become  the  larger 
and  dominant  one.      Similarly,  the  group  "  Jews  "  will 
change  from  a  dominant  group  into  a  subordinate  one, 
if  we  think  of  the  larger  group,  "European."      Now 
these  conceptions  of  dominant  and  subordinate  groups 
are    respectively   characterised    by    certain    differences. 
Thus    the    difference    between  "  Jews "  generally  and 
"  those  of  Middlesex,"  consists  in  the  latter  inhabiting 
that  county. 

There  are  also  certain  qualities  which  are  essential,  or 
proper,  to  objects,  and  others  which  belong  to  them  only 

*  See  ante,  p.  190. 


LOGIC  287 

accidentally.  Thus  a  Jew  is  a  man  who  believes  himself 
bound  to  keep  a  Sabbath,  and  this  is  "  essential/'  but 
he  may  be  lame  or  have  had  his  hair  cut  short,  cha- 
racters which  are  but  "  accidental  "  ones.  So  it  is  that, 
in  logic,  there  are  certain  names  which  can  only  be 
asserted,  or  predicated,  of  things,  according  to  the  mode  in 
which  the  mind  regards  them.  They  are  therefore 
called  predicables,  and  there  are  five  of  them — (i)  genus  ; 
(2)  difference ;  (3)  species;  (4)  property;  and  (5)  acci- 
dent. 

The  predicable  "  genus "  is  applied  to  any  larger 
group  which  includes  other  groups  within  it,  to  every 
one  of  which  it  applies,  and  each  one  of  which  is,  in 
logic,  termed  a  "  species."  Thus  in  the  first  of  the 
above  examples  "  Jew  "  is  a  genus  which  includes  the 
minor  groups  or  species — "  certain  men  of  Middlesex," 
"  certain  men  of  Essex,"  <fcc. — to  each  of  which,  that 
which  the  name  of  the  genus  denotes,  is  applicable. 
The  term  "  Jews  of  Middlesex,"  again,  is  also  a  genus, 
including  within  it  subordinate  groups  or  species,  such 
as  "  reformed  Jews "  and  "  unreformed  Jews,"  while 
"  European "  may  also  be  a  genus,  whereof  Jew, 
Englishman,  Russian,  &c.,  are  species, 

Thus  genus  and  species  in  logic  are  very  different 
from  genus  and  species  as  these  terms  are  used  by 
zoologists  and  botanists.* 

In  those  sciences  one  set  of  groups  is  always  genera, 
and  others  are  always  species,  and  none  can  be  both 
genus  and  species.  But  in  logic,  groups  are  not  always 
one  or  the  other,  but  may  be  either,  according  to  the 
direction  taken  by  thought,  as  we  see  "  Jew  "  may  be  a 
getms,  with  respect  to  "men  of  Middlesex,"  "  Essex," 

*  See  ante,  p.  190, 


288  ELEMENTS   OF  SCIENCE 

&c.,  but  it  may  be  equally  a  species,  with  respect  to  the 
concept  and  name  "  European." 

Thus  let  the  circle  A  (Fig.  54)  represent  the  genus 
"Jew,"  and  B  the  differentiating  quality  "man  of 
Middlesex,"  then  these  by  their  intersection  will  con- 
stitute C — i.e.,  the  species  "  Jew  of  Middlesex." 

On  the  other  hand,  A  may  represent  the  genus  "  man 
of  Middlesex,"  and  B  the  quality  "  Jew,"  with  the  same 
result  with  respect  to  C.  Thus  the  genus  and  the 
differential  quality  or  "  difference  "  may  change  places. 

Again  B  may  be  the  genus  u  man,"  and  A  the  quality 
FIG.  54. 

B 


"  hereditary  observer  of  the  Mosaic  Law,"  when  C  will 
be  "  Jew"  as  a  species. 

A  logical  definition  of  any  concept  is  formed  by 
uniting  the  proximate,  or  lowest,  genus  in  which  it 
is  contained,  with  its  differential  quality. 

The  lowest  species  can  never  be  a  genus,  and  consists 
only  of  the  individuals  which  compose  it.  Similarly  the 
highest  genus  can  never  be  a  species  because,  being  the 
highest,  it  cannot  be  included,  as  a  subordinate  group, 
within  any  higher  one. 

Between  the  highest  genus  and  the  lowest  species  are 
a  multitude  of  genera  which  are  called  subalternate, 


LOGIC  289 

because  (as  in  the  above  examples)  they  may  be  either 
genera  or  species  according  to  the  way  in  which  they 
are  used,  owing  to  the  direction  taken  by  thought. 
Thus  the  term  "  corporeal "  is  a  species  of  the  higher 
group,  the  genus  "  substance,"  while  it  is  a  genus  of  the 
lower  group,  "  living  creatures,"  which  is  here  a  species. 
That  species,  however,  becomes,  in  turn,  a  genus  if  we  take 
it  in  connection  with  ''animals"  and  "plants,"  both  of 
which  are  species  of  the  genus  "living  creature."  " Plant" 
in  turn  will  become  a  genus,  whereof  the  species  "flower- 
ing "  and  "  non-flowering  "  plants  are  species,  and  so  on. 
The  attributes  of  the  higher  group,  can,  of  course,  be 
affirmed  of  every  member  of  all  the  lower  groups  which 
are  included  within  it,  as  "corporeity"  can  be  affirmed 
of  all  living  creatures,  all  animals  and  all  plants,  and  all 
the  various  more  and  more  subordinate  groups  of  either. 
But  the  higher  the  group,  the  fewer  the  number  of 
attributes  which  can  be  affirmed  of  all  its  component 
members,  although  the  larger  it  is,  the  greater  the 
number  of  such  component  members  will  be.  On  the 
other  hand,  the  smaller  and  more  subordinate  the  group, 
the  greater  the  number  of  common  characters  possessed 
by  its  component  members.  Thus  the  group  "  apple 
tree,"  though  it  comprises  almost  infinitely  fewer  com- 
ponent members  than  the  group  "living  creatures," 
nevertheless  possesses  an  almost  infinitely  greatei 
number  of  common  characters  than  the  group  "  living 
creatures "  possesses ;  for  a  vastly  greater  number  of 
properties  are  common  to  all  apple  trees  than  are 
common  to  the  enormous  group  "  living  creatures," 
which  includes  everything  between  a  mushroom  and  a 
man.  A  difference  of  this  kind  is  expressed  by  the  terms 
extension  and  intension.  "  Extension "  refers  to  the 
number  of  groups  contained  within  a  concept ;  "  in- 

T 


290  ELEMENTS   OF   SCIENCE 

tension "  to  the  number  of  common  characters  which 
any  group  we  think  of  may  possess.  Thus  the  concept 
"  living  creature,"  has  enormous  "  extension  "  and  but 
little  "  intension,"  while  the  concept  "  apple  tree  "  has 
very  great  "  intension  "  and  but  little  "extension" — 
since  it  includes  no  living  creatures  whatever  save  apple 
trees.  Thus  the  greater  the  "  extension  "  the  less  the 
"  intension,"  and  vice  versa. 

A  concept  is  denned  in  logic  by  means  of  the  lowest 
genus  which  contains  it,  and  the  difference  which 
separates  it  oft'  from  the  other  species  of  that  genus,  as 
illustrated  in  Fig.  54. 

For  all  other  matters  which  concern  the  first  part  of 
logic,  the  reader  is  referred  to  works  upon  that  science. 

The  second  part  of  logic  treats,  as  before  said,  of 
judgments.  What  a  judgment  in  itself  is,  we  have 
already  seen.*  When  expressed  in  words  it  is  termed 
an  "  enunciation  "  or  "  proposition." 

A  proposition  is  an  expression  unambiguously  affirm- 
ing, or  denying,  one  thing  of  another,  and  it  consists  of 
three  parts,  two  of  these  are  termed  respectively  (i)the 
subject;  and  (2)  the  predicate  ;  the  third  is  the  copula. 

The  subject  is  that  term  of  which  the  other  is  affirmed, 
as,  e.g  ,  in  the  proposition  "  virtue  is  admirable,"  "  virtue  " 
is  the  subject.  The  predicate  is  that  term  which  is  affirmed 
of  the  other — as  "admirable"  is  affirmed  of  virtue.  The 
copula  is  the  term  which  connects,  or  couples,  the  subject 
and  the  predicate,  and  it  is  expressed  by  the  term  "  is." 

Each  term  may  consist  of  many  words,  as,  e.g,  "  To  rise 
early  in  the  morning  and  take  a  cold  bath  is  healthy." 
Here,  then,  the  eleven  words  which  precede  "  is  "  together 
constitute  one  term. 

*  See  ante,  p.  255. 


LOGIC  291 

Propositions  may  be  categorical  or  hypothetical,  and  the 
latter  may  be  either  conditional  (as,  if  X  then  Y),  or 
disjunctive  (as,  either  X  or  Y). 

"Categorical"  propositions  may  be  universal  or 
particular,  and  each  of  them  may  be  either  affirmative  or 
negative.  Thus  every  categorical  proposition  is  either : 

A  universal   affirmative   which    may    be  repre- 
sented by A. 

(e.g.,  all  whales  are  mammals.) 
A  universal  negative E. 

(e.g.,  no  whales  are  fishes.) 
A  particular  affirmative I. 

(e.g.,  some  whales  are  toothed.) 
A  particular  negative O. 

(e.g.   some  whales  are  not  toothed.) 

Propositions  which  differ  as  to  being  universal  or 
particular,  are  said  to  differ  in  quantity.  Those  which 
differ  as  to  being  affirmative  or  negative,  are  said  to  differ 
in  quality. 

Four  kinds  of  opposition  may  thus  exist  between 
judgments, and  they  may  be:  (i)  Contradictories;  (2)  Con- 
traries; (3)  Subcontraries ;  or  (4)  Subalterns. 

A  Contraries  E 


OS 


0,        y 

\  ^      | 


Subcontraries  O 


292  ELEMENTS   OF   SCIENCE 

When  a  universal  affirmative  and  a  particular  nega- 
tive (A  and  0)  or  a  particular  affirmative  and  a  universal 
negative  (I  and  E)  are  opposed,  they  are  "  contradictories," 
because  they  differ  both  in  quantity  (one  being  universal 
and  the  other  particular),  and  also  in  quality  (one  being 
affirmative  and  the  other  negative) :  e.g.,  "  All  men  are 
reasonable  beings"  and  "some  men  are  not  reasonable 
beings,"  or  "  Some  men  are  able  to  rise  in  the  air  "  and 
"  no  men  are  able  to  rise  in  the  air."  With  contradic- 
tories, both  cannot  be  true  and  both  false,  but  always  one 
true  and  the  other  false. 

When  a  universal  affirmative  and  a  universal  negative 
(A  and  E)  are  opposed  they  are  termed  "  contraries." 
They  differ  from  each  other  in  quality  only  and  not 
in  quantity,  because  they  are  both  universals ;  as  e.g., 
"All  plants  are  sensitive"  and  "no  plants  are  sensi- 
tive." Contraries  may  both  be  false,  but  they  cannot 
both  be  true. 

When  a  particular  affirmative  is  opposed  to  a  particular 
negative  (I  and  0)  they  are  called  "  subcontraries  "  and 
differ  as  to  quality  only,  both  being  particular,  and 
therefore  the  same  in  quantity;  as  e.g.,  "Some  men 
are  soldiers "  and  "  some  men  are  not  soldiers." 
Subcontraries  may  both  be  true,  but  they  cannot  both 
be  false. 

When  a  universal  affirmative  and  a  particular  affirm- 
ative (A  and  I),  or  a  universal  negative  and  a  particular 
negative  (E  and  0)  are  opposed,  they  are  named  "sub- 
alterns." They  are  opposed  in  quantity  only  (each  pair 
consisting  of  one  universal  and  one  particular  proposition) 
and  not  in  quality  (one  pair  being  both  affirmative  and 
the  other  pair  both  negative) ;  as  e.g.,  "  All  men  are 
mortal"  and  "  some  men  are  coal-heavers,"  or  "  No  men 
have  tails "  and  "  some  men  have  not  snub-noses." 


LOGIC  293 

Subalterns  may  both  be  false  and  both  true,  or  one  may 
be  false  and  the  other  true  in  either  case. 

A  term  is  said  to  be  distributed,  when  it  includes  every 
individual  of  the  class  to  which  it  refers.  Thus,  when  we 
say  "  fixed  stars  twinkle  "  and  "  no  man  can  fly,  "we  mean 
to  include  the  whole  of  the  fixed  stars  in  one  case,  and  all 
men  in  the  other. 

In  all  universal  propositions,  the  subject  is  distributed 
— as  in  the  instances  just  given.  In  all  negative  proposi- 
tions, the  predicate  is  distributed — as  "  Men  are  not 
immortal  "and  "some  whales  are  not  toothed."  "Im- 
mortal "  is  distributed  because  it  refers  to  all  men,  and 
"not  toothed"  is  distributed  because  it  refers  to  all  those 
whales  which  are  referred  to  and  included  in  the  above 
proposition. 

Therefore  in  universal  negative  propositions,  both 
terms  are  distributed,  while  in  particular  affirmative 
propositions,  neither  term  is  distributed. 

Propositions  can  be  inverted ;  that  is,  the  two  terms  of 
a  proposition  can  be  transposed,  and  this  process  is 
termed  conversion.  In  order  that  this  may  be  carried  out 
validly,  no  term  must  be  distributed  in  the  converted 
proposition,  which  was  not  distributed  before  its  con- 
version. 

Since  in  universal  negatives  (E)  both  terms  are 
distributed,  e.g.,  "  No  horses  are  winged  creatures," 
and  in  particular  affirmatives  (I)  neither  term  is 
distributed,  e.g.-,  "Some  horses  are  lame,"  therefore 
in  both  these  cases  the  terms  can  be  simply  trans- 
posed and  yet  the  propositions  must  remain  true — as 
"winged  creatures  are  not  horses"  and  "  lame  are  some 
horses." 

A  universal  affirmative  (A)  may  be  converted  by 
changing  it  into  a  particular  affirmative  (I),  as,  "  All  men 


294  ELEMENTS  OF   SCIENCE 

are  animals  "  may  be  converted  thus  :  Some  animals  are 
men. 

A  particular  negative  proposition  (0)  can  only  be 
converted  by  a  threefold  process  which  consists  in 

(1)  changing   the  copula  from  negative  to  affirmative; 

(2)  inverting  the  terms;  and  (3)  changing  the  subject 
into   the    term    contradictory    to  it.      Thus,   e.g.,   the 
proposition : 

"  Some  animals  are  not  apes,"  may  be  changed  by — 

(1)  Change  of  copula,  "  Some  animals  are  apes." 

(2)  Inversion  of  terms,  "Apes  are  some  animals." 

(3)  Changing  subject  into  its  )     "Not  apes  are  some 

contradictory,  /          animals." 

The  third  part  of  logic  concerns  reasoning,  which  may 
be  either  inductive  or  deductive.  Inductive  reasoning 
has  been  and  will  again  be  referred  to.* 

"  Deductive  reasoning,"  or  ratiocination,  consists  in 
the  discovery  of  the  relation  of  one  thing  to  another,  by 
means  of  the  relations  they  each  bear  to  some  third 
thing.  This  is  effected  through  the  juxtaposition  of 
two  propositions  in  such  a  manner  that  a  third  proposi- 
tion is  seen  to  follow  necessarily  from  them.  The 
essence  of  the  process  (and  perception)  exists  in  the 
word  therefore,  which  expresses  the  " inference"  and 
that  its  truth  is  a  necessary  consequence  of  what  has 
been  before  laid  down — the  third  proposition  being 
certainly  and  necessarily  true,  if  the  two  preceding 
propositions  are  themselves  true. 

These  three  propositions  must  not  contain  more  than 
three  terms.  Each  of  the  first  two  of  the  three  pro- 

"*  See  ante,  p.  260,  and  post,  p.  309. 


LOGIC  295 

positions  is  called  a  premiss,  while  the  third,  which  results 
from  them,  is  the  conclusion. 

Such  an  arrangement  of  propositions  is  termed  a 
syllogism,  and  its  three  terms  have  distinct  names. 

(1)  The  term  which  is  the  predicate  of  the  conclusion 
is  called  the  major  term  (A). 

(2)  That  which  is  the  subject  of  the  conclusion  is  named 
the  minor  term  (B). 

(3)  The  third  term  is  called  the  "  middle  term,"  because 
it  is  present  in  each  premiss,  but  not  in  the  conclusion. 

The  three  propositions  also  have  each  a  distinct 
name. 

(1)  One  is  named  the  major  premiss,  because  it  con- 
tains the  major  term. 

(2)  Another  is  the  minor  premiss,  because  it  contains 
the  minor  term. 

(3)  The  third  is  (as  above  said)  called  the  conclusion, 
and  it  declares   the  relation  of  the  major  and  minor 
terms  to  each  other. 

Thus  in  the  syllogism  : 

All  men  are  mortal. 
Socrates  is  a  man. 
Therefore  Socrates  is  mortal. 

"  Mortal "  is  the  major  term  because  it  is  the  predicate 
of  the  conclusion  (i.e.,  is  asserted  of  the  other  term  in 
the  conclusion),  and  therefore  the  first  proposition  is  the 
major  premiss. 

Similarly  the  second  proposition  is  the  minor  premiss, 
because  it  contains  the  minor  term  "  Socrates,"  which 
is  the  minor  because  it  is  the  subject  of  the  conclusion — 
i.e.,  is  the  term  of  which  the  predicate  " mortal"  is 
asserted. 


296  ELEMENTS  OF   SCIENCE 

"  Man  "  is  the  middle  term,  because  it  exists  in  both 
premisses  and  nob  in  the  conclusion. 

The  "  major  premiss  "  compares  the  major  term  with 
the  middle  term. 

The  minor  premiss  compares  the  minor  term  with  the 
middle  term. 

The  conclusion  compares  together  the  major  and  minor 
terms. 

The  validity  of  the  whole  process  reposes  upon  the 
truth  that,  whatever  can  be  affirmed  or  denied  of  a  class 
of  things  (i.e.,  of  every  member  of  it  considered  as  a 
whole  mass)  can  be  affirmed  or  denied  of  each  individual 
member  which  constitutes  it. 

The  truth  of  this  in  each  case  is  signified  by  the  word 
"  therefore" — expressed  or  understood. 

There  are  ten  Rules  with  respect  to  syllogisms. 

(i)  and  (2)  affirm  that  (as  before  said)  there  must  be 
neither  more  nor  less  than  three  terms  and  three 
propositions. 

(3)  The  middle  term   must   be   distributed   at   least 
once. 

(4)  No  term  must  be  distributed  in  the  conclusion 
which  was  not  so  in  the  premisses. 

(5)  There  must  not  be  two  negative  premisses. 

(6)  If  there  is  a  negative  conclusion  there  must  be  a 
negative  premiss. 

(7)  If  there  is  a  negative  premiss  there  must  be  a 
negative  conclusion. 

(8)  There  must  not  be  two  particular  premisses. 

(9)  If  there  is  a  particular  conclusion  there  need  not 
be  a  particular  premiss. 

(10)  If  there  is  a  particular  premiss  there  must  be  a 
particular  conclusion. 


LOGIC  297 

The  four  forms  of  categorical  propositions  (uni- 
versal and  particular  as  both  affirmative  and  nega- 
tive) we  have*  symbolised  by  the  letters  A,  E,  I,  0, 
as  denoting  the;  quantity  and  quality  of  propo- 
sitions. 

Syllogisms  are  said  to  differ  in  mood  when  they  differ 
with  respect  to  the  quantity  and  quality  of  their  com- 
ponent propositions.  Thus,  AAA  denotes  a  syllogism 
made  up  of  three  universal  affirmative  propositions,  and 
IEO  signifies  one  composed  of  a  particular  affirmative 
major  premiss,  a  universal  negative  minor  premiss,  and 
a  particular  negative  conclusion — "  as  Jones  is  a  man, 
no  man  is  without  a  backbone,  therefore  Jones  is  not 
without  a  backbone." 

There  are  sixty-four  possible  ways  of  arranging  three 
letters,  and  therefore  there  are  sixty-four  conceivable 
moods  for  syllogisms,  but  all  these  save  twelve  would,  if 
used,  sin  against  one  or  other  of  the  ten  rules  just  laid 
down. 

Syllogisms  are  further  said  to  differ  as  to  figure — that 
is,  according  to  the  position  of  the  middle  term,  and  there 
are  four  such  figures.  These  may  be  represented  by 
letters  which  serve  perfectly  to  represent  valid  syllogistic 
forms,  whatever  real  terms  may  be  substituted  for  such 
forms.  If  the  premisses  with  such  real  terms  be  actually 
true,  the  conclusion  necessarily  will  be  actually  true 
likewise. 

The  four  figures  may  also  be  represented  by  the 
following  diagrams,  which  portray  the  relative  extent 
and  relations  of  whatever  may  be  represented  by  the 
terms. 


*  See  ante,  p.  291. 


298  ELEMENTS   OF   SCIENCE 

First  Figure. — Here  the  middle  term  is  the  subject 
of  the  major  premiss  and  the  predicate  of  the  minor : 

All  M  is  A. 
But  all  B  is  M. 
Therefore  all  B  is  A. 

FIG.  55. 


Second  Figure. — Here  the  middle  term  is  the  predicate 
of  both  premisses : 

All  A  is  M. 
But  no  B  is  M. 
Therefore  no  B  is  A. 

FIG.  56. 


Third  Figure. — Here  the  middle  term  is  the  subject  of 
both  premisses ; 


LOGIC 

All  M  is  A. 
But  all  M  is  B. 

Therefore  some  B  is  A. 

f 

FIG.  57. 


299 


Fourth  Figure. — Here  the  middle  term  is  the  predicate 
of  the  major  premiss,  and  the  subject  of  the  minor : 

All  A  is  M. 
But  all  M  is  B. 
Therefore  some  B  is  A. 

FIG.  58. 


In  the  first  figure  the  valid  moods  are :   AAA,  All, 
EAE,  EIO.     AAI  and  EAO  are  also  valid  but  super- 


3oo 


ELEMENTS   OF   SCIENCE 


fluous,  because  the  former  is  contained  in  AAA  and  the 
latter  in  EAE. 

These  four  valid  moods  may  be  thus  represented. 

FIG.  59. 


The  last  of  the  four  moods  of  the  first  figure  will  run  : 

No  M  is  A. 

Some  B  is  M. 

Therefore  some  B  is  not  A. 

There  are  two  rules  for  syllogisms  of  the  first  figure. 

(1)  The  major  premiss  must  not  be  a  particular  pro- 
position. 

(2)  The  minor  must  not  be  negative. 


LOGIC 


301 


Thus,  if  in  the  above  syllogism  the  major  premiss 
were  "  some  M  is  A  "  the  middle  term  would  not  be 
distributed  in  either  premiss,  since  in  the  minor,  M  is 
only  affirmed  of  some  B  and  the  totality  of  M  is  not 
regarded  ;  therefore  the  third  rule  (p.  296)  is  violated. 

Again,  if  the  minor  was  negative  the  reasoning, 

No  M  is                  A 

(fish)  (feathered) 

Some  B  is  not              M 

(animal)  (fish) 

Therefore  some  B  is  not              A 

(animal)  (feathered) 

FIG.  61. 


would  be  invalid,  because  A  is  distributed  in  the  con- 
clusion but  not  in  the  mcyor  premiss — a  condition  techni- 
cally called  "an  illicit  process  of  the  major."  It  is 
evident  that  when  we  say  "No  M  is  A"  we  have  not, 
and  need  not  have,  in  view  an  extension  of  the  whole 
periphery  of  A.  What  we  say  is  that  the  whole  of  M 
has  been  surveyed  and  that  none  of  it  is  A.  But  when 


302  ELEMENTS   OF   SCIENCE 

we  say  "  Some  B  is  not  A  "  we  exclude  some  B  from 
the  entire  class  of  A,  and  so  A  is  distributed. 

Various  ingenious  plans  have  been  devised  whereby 
syllogisms  of  the  second,  third,  and  fourth  figures  qan 
be  converted  into  syllogisms  of  the  first  figure.  This 
process  reposes  upon  those  rules  for  the  conversion  of 
propositions  which  have  been  hereinbefore  given  (pp.  293 
and  294).  But  for  an  account  of  such  devices  the  reader 
is  referred  to  special  treatises  on  logic. 

In  the  second  figure,  the  valid  moods  are  :  AEE,  AGO, 
EAE,  and  EIO.  In  this  figure  there  must  be  a  negative 
premiss,  and  therefore  a  negative  conclusion.  Thus : 

All  apes  are  mammals. 

But  no  gill-bearing  creatures  are  mammals. 

Therefore  no  gill-bearing  creatures  are  apes. 

If  the  second  premiss  were  affirmative  as  well  as  the 
first,  the  middle  term  would  not  be  distributed,  as,  e.g., 
with  such  premisses  as  "  All  apes  are  mammals,"  and 
"  Hair-bearing  creatures  are  mammals,"  we  can  conclude 
nothing  because  the  middle  term  "  mammals  "  is  distri- 
buted in  neither  case.  For  all  that  appears,  there  might 
be  (as,  in  fact,  there  are)  mammals  which  are  neither 
"  apes  "  nor  "  hair-bearing  creatures." 

In  this  figure  also  the  major  premiss  must  not  be 
particular,  as  otherwise  there  would  be  a  term  distri- 
buted in  the  conclusion  which  was  not  distributed  in  the 
premiss,  and  this  is  against  Rule  4  (p.  296). 

The  third  figure  has  the  following  valid  moods  :  AAI, 
All,  EAO,  EIO,  IAI,  OAO.  Here  there  must  be  no 
negative  minor,  but  there  must  be  a  particular  conclu- 
sion. Thus : 

All  mammals  have  warm  blood. 

But  all  mammals  are  air-breathers. 

Therefore  some  air-breathers  have  warm  blood. 


LOGIC  303 

If  the  minor  was  negative,  as,  e.g.,  "  All  mammals  are 
not  furnished  with  gills,"  we  could  not  thence  conclude 
that  "  Some  creatures  not  furnished  with  gills  have  warm 
blood,"  because  the .  term  "  furnished  with  gills  "  is  dis- 
tributed in  the  conclusion  but  not  in  the  minor  premiss, 
since  there  may  be  and  are  creatures  "  not  furnished 
with  gills  "  which  are  not  "  mammals."  This  would  be 
an  "  illicit  process  of  the  minor." 

Similarly,  there  must  be  a  particular  conclusion,  as 
otherwise  our  conclusion  would  be  "All  air-breathers 
have  warm  blood,"  in  which  case  the  term  "  air- 
breathers"  would  be  distributed  in  the  conclusion,  but 
not  in  the  minor  premiss,  which  only  says  that  "All 
mammals  are  air-breathers,"  for  all  which  it  may  be 
the  case  (as  it  is)  that  many  air-breathers  are  not 
mammals. 

The  valid  moods  of  the  fourth  figure  are,  AAI,  AEE, 
EAO,  EIO,  IAI. 

In  this  figure,  when  the  major  is  affirmative,  the  minor 
must  be  universal ;  and  when  the  minor  is  affirmative, 
the  conclusion  must  be  particular.  Thus  : 

All  apes  are  mammals. 

All  mammals  have  backbones. 

Therefore  some  backboned  mammals  are  apes. 

If  for  the  minor,  we  only  had  "  some  mammals  have 
backbones,"  we  could  not  know  from  our  syllogism 
whether  apes  might  not  be  mammals  without  backbones. 
In  order  that  a  conclusion  in  this  figure  should  be  uni- 
versal, we  require  a  negative  minor.  Thus : 

All  apes  are  mammals. 

No  mammals  breathe  by  gills. 

Therefore  no  creatures  breathing  by  gills  are  apes. 

The  division  of  syllogisms  into  these  figures  is  not  a 


304  ELEMENTS   OF   SCIENCE 

mere  useless  trick  of  art ;  for  one  figure  is  more  useful 
for  some  purposes  than  another,  though  generally  the 
first  figure  is  the  best  and  most  serviceable.  It  is 
more  convenient,  e.g.,  to  say  "Our  judges  are  not 
untrustworthy  and  corrupt,"  than  it  is  to  say  "  no 
men  who  are  untrustworthy  and  corrupt  are  judges." 
If  we  wish  to  show  how  some  men  will  labour 
earnestly  to  give  just  decisions  without  private  reward, 
we  may  say : 

Our  judges  la.bour  earnestly  to  give  just  decisions. 

Our  judges  will  accept  no  private  reward. 

Therefore  some  men  who  will  accept  no  private  re- 
ward will  labour  earnestly  to  give  just  decisions  ; 
which  is  a  syllogism  of  the  third  figure  and  the  mood 
AAI. 

But  the  utility  of  the  rules  concerning  syllogisms  may 
perhaps  be  made  more  evident  by  some  examples  of  their 
violation.  Thus : 

The  temperate  are  healthy. 

Some  ignorant  people  are  healthy. 

Therefore  some  ignorant  people  are  temperate. 

This  is  a  syllogism  of  the  second  figure  and  the  mood 
All,  but  there  is  no  such  valid  mood,  and  in  fact  it  is 
but  a  syllogism  in  appearance,  for  the  middle  term  is 
not  distributed  in  either  premiss.  It  does  not  declare 
that  all  healthy  people  are  either  temperate  or  igno- 
rant, and  so,  for  all  it  says,  there  may  be  some  (as 
in  fact  there  are)  who  are  neither  the  one  nor  the 
other.  Again : 

Men  of  science  are  learned  men. 
Men  of  science  are  long-lived  men. 
Therefore  all  long-lived  men  are  learned  men. 


LOGIC  305 

This  is  a  syllogism  of  the  third  figure  and  the  mood 
A  A  A,  but  there  is  no  valid  mood  of  that  kind  in  the 
third  figure  which  needs  a  particular,  not  a  universal, 
conclusion.  The  Above  apparent  syllogism  is  invalid- 
There  is  in  it  an  "  illicit  process  of  the  minor,"  the  term 
"  long-lived  men  "  not  being  distributed  in  the  minor 
premiss,  though  it  is  in  the  conclusion. 

A  Demonstration  is  a  syllogism,  the  major  term  of 
which  denotes  a  "property,"  the  minor  the  "species," 
and  the  middle  term  the  definition*  of  a  species. 
Thus: 

A  rational  animal  is  capable  of  laughter. 

Man  is  a  rational  animal. 

Therefore  man  is  capable  of  laughter. 

But  all  syllogisms  are  objected  to  by  some  people  who 
affirm  that  they  teach  us  nothing,  because  the  conclusion 
of  a  syllogism  only  re-affirms  what  was  already  contained 
in  its  premisses.  "  Whoever  has  said,"  they  repeat,  that 
"  all  men  are  mortal "  has  already  said  in  effect  that 
"Socrates  is  mortal." 

To  test  the  force  of  this  objection,  let  us  see  by  an 
example  what  our  meaning  is  when  we  declare  that  any 
one  object  belongs  to  a  certain  class  of  objects.  Persons 
ignorant  of  zoology,  may  fancy  that  a  whale  is  a  fish. 
Nevertheless  the  whale  in  truth  belongs  to  the  class  of 
beasts.  Now  when  we  make  that  statement  what  do  we 
mean  ?  We  mean  that  a  whale,  in  spite  of  its  shape  and 
exclusively  marine  mode  of  life,  is  nevertheless  more 
closely  allied  in  its  nature  to  such  creatures  as  cattle, 
beasts  of  prey,  &c.,  than  it  is  to  any  fishes.  But  even  if 
we  are  zoological  experts,  we  do  not,  in  saying  "  a  whale 

*  See  ante,  p.  288. 


306  ELEMENTS   OF  SCIENCE 

is  a  beast,"  distinctly  advert  in  our  minds  to  all  those 
various  anatomical  conditions  which  characterise  the 
class  of  beasts,  but  only  to  the  fact  of  the  predominance 
in  the  whale's  organisation  of  the  marks  which  distin- 
guish that  class  of  animals.  We  can,  however,  if  we 
choose,  turn  back  our  mind,  and  mentally,  or  verbally, 
refer  to  any  one  of  such  marks  or  characters,  and  recog- 
nise the  fact  that  the  whale,  inasmuch  as  it  belongs  to 
the  class  of  beasts,  must  have  that  particular  character  so 
referred  to — one  of  those  various  marks  which  are  com- 
mon to  the  whole  class.  Then  we  may  say  to  ourselves, 
"The  whale,  being  a  beast,  must  have  warm  blood." 
We  in  this  manner  bring  forward  into  explicit  recogni- 
tion a  character,  the  existence  of  which  was  implicitly 
contained  in  the  statement  that  it  was  a  beast.  This 
character  may  not  only  have  never  been  previously 
thought  of  by  us,  but  we  may  not  have  recognised  the 
fact  at  all. 

In  repeating,  then,  the  syllogism  : 

All  beasts  have  warm  blood. 

The  whale  is  a  beast. 

Therefore  the  whale  has  warm  blood, 

a  new  fact  may  become  explicitly  recognised  which 
previously  was  but  latent,  and  so  the  syllogism  can 
impart  knowledge — it  makes  implicit  truth  explicit. 

Now  the  difference  between  explicit  and  implicit 
knowledge  is  so  great  that  the  latter  may  not  de£erve  to 
be  considered  "knowledge"  at  all.  No  one  will  affirm 
that  a  student  by  merely  learning  the  axioms  and  defini- 
tions of  Euclid,*  will,  by  having  done  so,  have  also 
become  at  once  acquainted  with  all  the  geometrical 

*•  See  ante,  p.  34. 


LOGIC  307 

truths  the  work  contains,  so  that  he  will  have  no  need 
to  study  its  various  propositions,  all  of  which  he  will 
thus  know  without  having  once  read  them.  Yet  all  the 
propositions  about  circles,  triangles,  &c.,  in  his  "Euclid" 
are  implicitly  contained  in  the  definitions  and  axioms. 
Although,  then,  a  student  may  know  that  mass  of  geo- 
metric truths  implicitly  (in  knowing  the  definitions  and 
axioms)  he  does  not  for  all  that,  really  and  actually 
know  them.  In  order  that  he  may  learn  truly  to 
know  them,  he  must  go  through  those  various  processes 
of  "  inference "  by  which  the  different  truths  implicitly 
contained  in  Euclid's  definitions  and  axioms  are  brought 
to  the  student's  knowledge  explicitly. 

After  this  digression  we  will  continue  and  conclude 
our  notice  of  the  elementary  rules  of  logic. 

One  form  of  argument  is  termed  a  Swites.  In  it  a 
number  of  propositions  are  so  heaped  up  together  that 
the  predicate  of  the  preceding  proposition  is  always 
taken  as  the  subject  of  the  following  one,  till  the  last 
predicate  is  enunciated  together  with  the  first  subject. 

Thus  we  may  have : 

Peter  is  a  man. 

All  men  are  animals. 

All  animals  are  living  things. 

All  living  things  are  corporeal. 

All  corporeal  things  are  substances. 

Therefore  Peter  is  a  substance. 

This  reasoning  really  consists  of  a  series  of  syllogisms, 
all  the  minor  terms  of  which,  except  the  first,  and  all 
the  conclusions,  except  the  last,  are  left  out.  All  the 
majors,  however,  the  first  minor  and  the  last  conclusion, 
have  been  retained,  while  the  retained  minor  and  the 
first  major  have  been  transposed,  the  minor  coming 


308  ELEMENTS   OF   SCIENCE 

first.     Thus,  written  out  fully,  the  abo\7e  sorites  would 
become : 

All  men  are  animals. 

Peter  is  a  man. 

Therefore  Peter  is  an  animal. 

All  animals  are  living  things. 

Peter  is  an  animal. 

Therefore  Peter  is  a  living  thing. 

All  living  things  are  corporeal. 

Peter  is  a  living  thing. 

Therefore  Peter  is  corporeal. 

All  corporeal  things  are  substances. 

Peter  is  a  corporeal  thing. 

Therefore  Peter  is  a  substance. 

[The  propositions  in  black  type  are  the  ones  left  out  in 
the  sorites.] 

Another  form  of  reasoning,  in  which  there  are  at  most 
two  hidden,  or  cryptical,  syllogisms,  is  called  a  Pro- 
syllogism,  Thus : 

All  tyrants,  because  they  transgress  the  law,  are 
unjust,  but  Napoleon  I.,  who  violated  his  engage- 
ments to  the  Republic  to  make  himself  supreme, 

was  a  tyrant,  therefore  Napoleon  I.  was  unjust. 

[The  parts  in  black  type  are  relics  of  two  hidden  or 
cryptical  syllogisms.] 

Thus  written  out  at  length  the  prosyllogism  is : 

All  who  transgress  the  law  are  unjust. 

But  tyrants  transgress  the  law. 

Therefore  tyrants  are  unjust. 

All   who  violate   their   engagements    to 

the    Republic    to    make    themselves 

supreme  are  tyrants. 


LOGIC  309 

But  Napoleon  I.  violated  his  engagements  to 

the  Republic  to  make  himself  supreme. 
Therefore  Napoleon  I.  was  a  tyrant. 
All  tyrants  are  unjust. 
Napoleon  I.  was  a  tyrant. 
Therefore  Napoleon  I.  was  unjust. 

Syllogisms  may  also  be  hypothetical  instead  of  cate- 
gorical, and  hypothetical  syllogisms  may  be  conditional 
or  disjunctive. 

The  following  is  their  form  : 

(1)  Conditional: 

If  A  is  B  then  C  is  D. 
(Antecedent)     (Consequent) 
or  if  A  is  B  then  A  is  C 

but  A  is  B  therefore  A  is  C. 

or  finally  if  A  is  B  then  A  is  C. 
but  if  A  is  D  then  A  is  B. 

therefore  if   A  is  D  then  A  is  C 

(2)  Disjunctive  syllogisms  are  thus  expressed  : 
either  A  is  B  or  C  is  D. 

or  either       A  is  B  or  A  is  C. 

A  dilemma  is  a  particular  form  of  "  disjunctive  "  syl- 
logism, e.g., 

If  A  is  B  then  either  C  is  D  or  E  is  F. 
but  neither  C  is  D  nor  E  is  F. 
therefore       A  is  not  B. 

Induction  *  does  not  depend  on  the  syllogistic  principle, 
but  on  a  belief  in  the  order  and  continuity  of  nature. 

*  See  ante,  pp.  260  and  294. 


3io  ELEMENTS   OF   SCIENCE 

It  is  true  that  the  dictum  "whatever  you  can  assert 
of  all  things  contained  under  a  class,  can  be  asserted  of 
that  class."  This  is  manifest,  obvious,  and  even  trivial, 
and  of  no  practical  value. 

The  form  of  induction  is  as  follows  :— 

a  +  b  +  c       is  Z. 
but  a  +  b  +  c  =  all  X. 

therefore  X  is  Z. 

It  is,  however,  only  in  very  rare  instances  that  a  +  b  +  c 
are  all  X. 

The  practical  dictum  of  induction  is  :  "  What  you  can 
say  of  a  sufficient  number  of  particulars  of  any  class 
under  a  required  diversity  of  circumstances  and  condi- 
tions, you  can  fairly  predicate  of  the  whole  class."  It  is 
the  main  process  used  in  the  development  of  the  physical 
sciences. 

It  is  the  process  of  discovering  laws  from  facts,  and 
causes  from  effects. 

a  +  b  +  c  is  Z, 

but  a  +  b  +  c  though  not  all  X  may,  from  the  peculiarity 

of  their  circumstances,  be  taken  as  practically  =  all  X, 

therefore  X  is  Z. 

Deduction,  as  we  have  now  seen,  derives  facts  from  laws, 
and  effects  from  causes. 

We  all  notice,  with  more  or  less  readiness  and  facility, 
resemblances  and  differences,  and  we  group  these  in 
relation  to  their  antecedents  and  consequences.  As  an 
example,  we  may  take  the  fact  before  noticed  *  that 
while  almost  all  bodies  tend  to  fall,  they  fall  differently 
in  the  open  air  and  under  the  bell-glass  of  an  air  pump. 

We  study  nature  always  by  observations,  but  we  can 

*  See  ante,  p.  60. 


LOGIC  311 

often  so  arrange  the  conditions  of  bodies  as  to  make 
experiments  with  them.  The  latter  process  is  especially 
useful  in  studying  the  cause  of  any  action,  or  condition, 
of  bodies. 

The  cause  (or  causes)  of  anything  must  be  sought 
amongst  its  invariable  antecedents  or  concomitants. 

The  circumstances  in  which  all  the  instances  in  which 
anything  takes  place,  alone  agree,  must  be  a  cause.  This 
is  called  the  method  of  agreement. 

If  two  instances  have  all  their  circumstances  alike 
save  one,  and  the  event  (the  cause  of  which  is  sought) 
only  occurs  in  that  single  case,  then  that  one  must,  at 
the  least,  be  closely  related  to  its  cause.  This  is  the 
method  of  difference. 

If  two  instances  in  which  Y  occurs  have  X,  and  two 
instances  in  which  Y  does  not  occur,  have  nothing  in 
common  but  the  absence  of  X,  then  X  is  the  cause  of 
Y.  This  is  the  joint  method  of  agreement  and  difference. 

If  we  subtract  from  a  given  effect,  all  that  is  due  to 
certain  causes,  then  the  residue  is  the  effect  of  the  rest  of 
the  causes.  This  is  the  method  of  residues. 

If  X  and  Y  increase,  decrease,  and  vary  together, 
then  one  is  the  cause  of  the  other,  or  closely  connected 
with  such  cause.  This  is  the  method  of  concomitant 
variations. 

One  effect  may  have  several  causes,  therefore  the 
method  of  agreement  is  uncertain,  but  not  so  "  the  joint 
method  of  agreement  and  difference." 

A  cause  is  generally  suggested  by  analogy,  or  resem- 
blance, from  cases  in  which  the  connection  of  a  cause  and 
effect  is  better  known. 

A  cause  will,  as  a  rule,  be  the  more  easily  discovered, 
the  greater  the  number  of  forms  of  the  effect  which  are 
examined. 


312  ELEMENTS   OF  SCIENCE 

A  suspected  cause  may  be  tested  by  allowing  it  to 
operate  in  circumstances  of  less  complication,  to  see 
whether  the  effect  will  still  be  produced. 

Such  are  the  main  practical  rules  which  should  be 
made  use  of  when  applying  the  inductive  method  in 
practice. 

The  chief  part  of  logic,  however,  is  the  deductive 
system  (the  elements  of  which  have  been  described  in 
this  chapter),  which  therefore,  as  before  said,  especially 
constitutes  both  the  science  of  the  laws  of  thought,  and 
the  art  of  reasoning. 


CHAPTEK  IX 
HISTORY 

BY  History  we  mean  an  account  of  those  successive 
conditions  and  inter-relations  of  different  nations,  which 
are  based  upon  more  or  less  trustworthy  evidence.  It 
includes  an  account  of  religion,  speculative  opinions, 
language,  manners  and  customs,  &c.,  as  well  as  of 
migrations,  wars,  political  organisations  and  the  suc- 
cession of  different  dynasties.  This  vast  mass  of  in- 
formation cannot,  it  is  obvious,  be  sketched,  even  most 
briefly,  in  a  single  chapter — least  of  all  in  a  chapter  of 
such  an  elementary  work  as  the  present  one.  Various 
branches  of  inquiry  must  be  here  passed  over  entirely  in 
silence,  while  others  can  be  little  more  than  hinted  at, 
though  the  elements  of  historical  science  must  not  be 
altogether  omitted.  But  the  reader  is  referred  to 
special  treatises  on  the  history  of  different  nations,  on 
philology,  on  manners  and  customs,  on  religion  and  on 
philosophy,  for  all  that  he  may  desire  further  to  know 
on  so  extremely  important  a  subject. 

There  are  some  persons  who  will  not  be  content  with  a 
mere  record,  even  a  full  one,  of  those  conditions  of  man- 
kind which  are  known  to  us  through  authentic  records 
(written  or  engraved  on  stone),  but  demand  an  account 
of  antecedent  periods  now  commonly  denoted  by  the 
term  "  prehistoric."  Others  go  further  still,  and  require 
a  statement  as  to  the  probabilities  respecting  the  origin 


314  ELEMENTS   OF   SCIENCE 

of  the  whole  human  race.  Such  a  question  as  this  last, 
however,  cannot  be  entered  upon  here,  any  more  than 
the  inquiry  as  to  the  origin  of  intellect  *  or  of  life,t  or 
the  absolute  nature  of  light  or  heat.J  The  facts  which 
have  been  herein  brought  before  the  reader's  notice,  are 
too  elementary  to  warrant  the  introduction  of  statements 
which  must  be  merely  speculative.  Persons  specially 
interested  in  the  question  as  to  what  light  science  throws 
upon  the  origin  of  man,  are  here  referred  to  an  ante- 
cedent publication  of  the  present  author.  §  We  may, 
however,  even  here,  point  out  that  since  thought  pre- 
cedes language  (whether  of  speech  or  gesture)  it  is 
impossible  to  understand  how  a  rational  being,  one 
especially  who  has  a  perception  of  right  from  wrong, 
could  ever  have  arisen  from  a  basis  of  mere  feeling,  and 
from  creatures  incapable  of  abstract  thought,  even  such 
thought  as  everywhere  exists  even  amongst  the  very 
lowest  savage  tribes.  ||  However  tempted  we  may  be  to 
assume  it,  it  is  also  by  no  means  evident  that  the  most 
barbarous  existing  savages  afford  us  the  best  attainable 
representation  of  the  very  earliest  condition  of  man- 
kind. 

Of  course  when  we  take  a  wide  view  of  all  human 
history  known  to  us,  it  becomes  plain  that,  on  the 
whole,  there  has  taken  place  a  process  which  we  must 
recognise  as  one  of  progress  and  improvement ;  yet  even 
with  respect  to  savages,  there  is  much  evidence  to  show 
that  very  many  of  them  have  fallen  from  some  higher 
Antecedent  condition.  Social  progress  is  an  exceedingly 
complex  phenomenon,  the  result  of  many  factors.  No 

*  See  ante,  p.  269.  t  See  ante,  p.  189. 

J  See  ante,  p.  86. 

§  The  "Origin  of  Human  Reason."     Kegan  Paul,  Trench, 

&  Co.,  1889.  ||  See  ante,  pp.  264  and  268. 


HISTORY  315 

one  will  probably  contest  that  in  some  matters  of  art, 
even  we  Europeans  have  fallen  far  behind  our  prede- 
cessors of  more  than  two  thousand  years  ago.  The  ruins 
which  exist  in  Central  America  demonstrate  the  degra- 
dation which  has  there  taken  place,  and  the  degradation 
of  various  tribes  of  American  Indians  is  certainly  known. 
The  Fuegians  and  Caffirs  also  give  evidence  that  they 
once  possessed  a  higher  social  state  than  is  theirs  to-day. 
The  world  is,  in  fact,  sown  broadcast  with  the  traces  of 
higher  social  conditions  and  civilisations  which  have 
passed  away,  and  bears  many  a  scar  due  to  the  triumph 
of  ignorance  and  brutality  over  relative  refinement  and 
culture. 

Putting  on  one  side,  then,  the  questions  which  regards 
the  very  earliest  condition  of  mankind,  it  has  been 
ascertained  that  many  races  have  passed  through  several 
prehistoric  stages  of  existence.  There  was  a  time  when 
the  only  weapons  made  use  of  by  such  races  were 
roughly  chipped,  unpolished  flint  implements.  These 
have  been  distinguished  as  Palceolithic  men.  Other  and 
later  races  formed  implements  of  ground  flint,  and  they 
have  been  termed  Neolithic  men.  Then  we  have  races 
which  made  use  of  metal  for  attack  and  defence ;  first  of 
weapons  formed  of  bronze,  on  which  account  they  have 
been  called  Bronze  men,  and  later  of  iron,  and  such 
last  have  been  named  after  that  metal. 

But  as  yet  there  is  very  insufficient  evidence  as  to  the 
length  of  time  during  which  palaeolithic  men  lived  in 
any  one  region,  nor  has  it  been  proved  that  palaeolithic 
and  neolithic  men  may  not  have  co-existed  in  different 
regions,  as  we  know  "bronze"  men  and  "iron"  men 
did  subsequently.  But  even  palaeolithic  men  could  make 
drawings  in  outline  of  different  animals,  and  we  owe  to 
them  the  only  authentic  representation  of  the  mammoth, 


316  ELEMENTS   OF   SCIENCE 

or  extinct  elephant,  scratched  on  one  of  that  animal's 
bones.  For  man  had  come  into  existence  while  various 
animals,  now  extinct,  still  inhabited  the  earth,  amongst 
them,  the  mammoth,  the  woolly  rhinoceros,  the  cave 
bear  and  the  cave  hyaena — so  called  because  their 
remains  have  been  found  in  caves,*  as  have  the  remains 
of  many  men. 

Thus  it  is  certain  that  the  earth  has  had  human 
inhabitants  for  a  long  period,  although  it  is  impossible 
as  yet  to  express  it  with  any  accuracy  in  terms  of  years 
— save  as  a  minimum.  The  civilisations  of  Egypt  and  of 
China  extend  back  for  more  than  six  thousand  years, 
but  they  were  probably  preceded  by  tens  of  thousands, 
possibly  by  hundreds  of  thousands,  of  years  of  un- 
recorded human  existence.  It  may,  however,  be  con- 
sidered certain  that  man  did  not  exist  before  the 
tertiary  epoch,  although  it  would  be  rash  to  deny  the 
possibility  of  his  having  appeared  in  "  Miocene  " 
times.* 

However  that  may  be,  many  naturalists  are  now 
convinced  that  man's  existence  antedates  the  glacial 
epoch,  and  it  is  certain  that  he  has  witnessed  great 
geographical  changes  and,  as  before  said,  the  extinction 
of  many  animals.  Some  of  these  must  have  been  formid- 
able enemies,  indeed,  to  men  armed  with  no  better 
weapons  than  were  the  ancient  flint  implements. 

We  must  not,  however,  linger  over  matters  prehistoric, 
but  advance  at  once  to  note  the  elementary  facts  of 
history,  and  especially  of  that  history  which  specially 
relates  to  the  existing  condition  of  our  nation  and  of  the 
nations  which  are  most  nearly  related  to  us.  Thus,  for 
our  present  purpose,  we  may  leave  entirely  on  one  side  the 

*  See  ante,  p.  169. 


HISTORY  317 

inhabitants  of  all  parts  of  the  earth  unknown  to  the 
government  of  the  ancient  Roman  Empire,  since  all 
Europe  is  the  outcome  of  Roman  civilisation  modified  by 
the  action  upon  it  of  the  inhabitants  of  the  provinces  it 
conquered  and  of  unconquered  regions  near  it. 

There  appears  much  reason  to  believe  that  one  stock, 
or  early  race,  of  mankind  was  the  common  parent  of 
almost  all  the  inhabitants  of  Europe,  Persia  and  India, 
and  this  race  has  been  distinguished  as  Indo-Germanic 
or  Aryan.  The  exceptions  are  the  Laps  and  Finns  of 
Northern  Europe,  the  Basques  of  the  South- West,  and 
the  Turks. 

The  Non-aryan  inhabitants  of  Asia  were  the  Turks, 
Mongols  and  Chinese,  together  with  the  very  remarkable 
people  known  as  Semites — remarkable  indeed  because 
amongst  them  rose  the  Jewish,  Christian  and  Mahom- 
medan  religions,  while  they  also  gave  origin  to  some  of 
the  grossest  and  most  cruel  forms  of  paganism.  The 
"Semitic"  nations  were  the  Jews,  the  Arabs,  and  the 
Phoenicians.  The  last  named  dwelt  on  the  sea  coast 
of  Syria,  whence  they  sent  forth  colonies,  the  most 
notable  of  which  was  Carthage,  though  some  were 
beyond  the  Straits  of  Gibraltar,  one  of  these  being  Cadiz. 
The  inhabitants  of  Africa  were  of  negro  race,  save  the 
Egyptians  in  the  north  (where  the  valley  of  the  Nile 
sheltered  and,  through  its  annually  rising  waters, 
nourished  them)  together  with  north-western  tribes  over 
which  Carthage  came  to  dominate. 

Of  the  Aryan  Europeans,  the  earliest  to  have  authentic 
historical  records,  and  the  most  famous  in  early  science, 
literature  and  art,  were  the  Greeks.  It  is  one  of  the 
most  wonderful  facts  of  history  that  so  small  a  people, 
inhabiting  so  restricted  a  territory  of  islands  and 
peninsulas,  mountains  and  valleys,  should,  almost 


318  ELEMENTS   OF   SCIENCE 

unaided,  have  developed  a  civilisation  which  has  ever 
since  been  the  admiration  of  the  most  cultured  of 
mankind,  and  which,  in  some  respects,  no  moderns  can 
equal,  far  less  surpass.  It  was  also  developed  with 
amazing  rapidity,  for  from  the  giving  of  laws  to  Athens 
by  Solon,  B.C.  594,  to  its  conquest  by  Philip  of  Macedon, 
was  but  a  period  of  little  more  than  two  hundred  and 
fifty  years.  The  Greeks  were  divided  into  a  number  of 
small  States,  the  most  celebrated  of  which  was  Attica 
(whereof  Athens  was  the  capital),  and  the  Peloponnesus, 
which  consisted  of  what  is  now  the  Morea,  with  Sparta 
for  its  capital. 

They  early  sent  out  colonies  to  Cyprus,  Sicily,  Southern 
Italy  and  the  South  of  France  (having  founded  there 
the  city  of  Marseilles)  and  in  many  parts  they  came  in 
hostile  contact  with  colonies  of  Phoenicians,  who  were  a 
people  yet  earlier  civilised,  hardy  and  indefatigable 
traders,  from  whom  the  Greeks  seem  to  have  learned 
their  alphabet  and  who  had  colonised  before  the  latter. 

Those  celebrated  poems,  the  "Iliad "and  the  "Odyssey," 
though  they  must  be  deemed  unhistorical,  are  yet  thought 
to  give  us  a  tolerably  faithful  picture  of  early  Greek  life. 

The  governments  of  the  different  Greek  States,  each 
of  which  was  the  dominion  of  a  city,  at  first  consisted  of 
an  hereditary  king,  a  council  of  chiefs,  and  a  more 
general  assembly  of  those  who  held  the  rights  of  citizen- 
ship. In  Greece  itself,  the  kingly  power  gradually  dis- 
appeared to  give  way  to  an  aristocratic  government  of 
privileged  families  (descendants  of  the  oldest  inhabitants) 
or  to  democracies — that  is,  government  by  the  citizens 
assembled.  These  citizens,  however,  were  by  no  means 
the  same  as  the  inhabitants  of  the  city,  but  only  a  wider 
aristocracy.  For  in  most  cities  there  were  many  slaves 
and  free  men  who  were  not  natives.  These  had  no  power 


HISTORY  319 

themselves,  nor  even  their  children,  till  they  were  made 
citizens. 

Sparta  retained  the  name  of  king  for  two  of  its 
hereditary  magistrates,  who  exercised  their  power  simul- 
taneously. The  two  States  north  of  what  was  at  first 
alone  deemed  true  Greece — namely,  Macedonia  and 
Epirus — retained  the  old  kingly  system  of  government. 

Besides  these  forms  of  government,  local  disputes  and 
disorders  sometimes  enabled  an  influential  citizen  to  seize 
supreme  power.  Such  a  man  was  called  a  tyrant,  and 
his  system  a  tyranny ;  though  such  expressions  did  not 
originally  denote  the  way  in  which  such  power  was  used, 
but  only  its  form.  The  last  notable  tyrant  in  Greece  itself 
was  Pisistratus,  whose  sons  were  expelled  about  the  end 
of  the  sixth  century  before  Christ.  In  the  colonies, 
however,  especially  in  Sicily,  they  existed  much  later. 

The  expulsion  from  Athens  of  Hippias,  son  of 
Pisistratus,  was  the  occasion  of  the  first  of  the  famous 
Persian  wars.  The  Persians  who,  under  Cyrus,  in  the 
sixth  century  B.C.,  took  the  great  and  powerful  city  of 
Babylon,  also  conquered  a  domain  which  included  Greek 
colonies  on  the  coast  of  Asia  Minor,  and  thus  became 
involved  in  disputes  with  Greece  itself.  Later,  the 
Persian  king,  Darius,  desiring  to  force  the  Athenians  to 
take  back  Hippias,  sent;  an  expedition  which  landed  in 
Attica,  but  was  utterly  defeated  B.C.  490,  in  the  celebrated 
battle  of  Marathon,  by  a  relatively  insignificant  for.ce  of 
skilled  and  well-disciplined  troops.  Ten  years  later,  the 
Persian  king,  Xerxes,  came  by  land  with  a  vast  army? 
only  to  be  routed  at  Thermopylae,  and  soon  the  Persians 
were  forced  to  withdraw  for  a  time  even  from  the  Greek 
cities  of  Asia. 

These  efforts  led  to  a  great  ascendency  of  Athens  in 
Greece.  It  was  a  very  democratic  State,  under  the 


320  ELEMENTS   OF   SCIENCE 

leadership  (from  444-429  B.C.)  of  Pericles,  who  adorned 
the  city  with  new  temples  and  other  public  buildings, 
while  the  poets,  ^Eschylus  and  Sophocles,  produced 
their  world-renowned  plays,  to  be  succeeded  later  by 
those  of  Euripides  and  Aristophanes.  This  also  was  the 
period  of  Socrates  and  Plato,  of  whom  we  have  to  speak 
later.  The  power  and  splendour  of  Athens  increased 
till  the  jealousy  of  other  great  cities  gave  rise  to  the 
celebrated  Peloponnesian  war  between  Athens  and 
aristocratic  Sparta,  with  their  respective  allies.  It 
lasted,  with  a  brief  interval,  for  twenty-nine  years,  and 
ended  in  the  defeat  of  the  Athenians  at  the  naval  battle 
of  Egospotamos.  But  the  subsequent  predominance  of 
Sparta  was  followed,  after  various  struggles,  by  the 
practical  subjugation  of  the  whole  of  Greece  under 
Philip,  King  of  Macedon,  whose  son,  Alexander  the  Great, 
as  the  leader  of  Greece,  invaded  and  conquered  Persia, 
received  the  submission  of  Egypt — where  he  founded 
Alexandria  —  and  after  penetrating  into  Northern 
India,  died  at  Babylon,  B.C.  323.  He  was  the  greatest 
conqueror  the  world  had  yet  known,  and  the  vast 
empire  he  erected  became,  after  his  death,  divided 
between  his  generals.  Thus  his  conquests  gave  rise  to 
the  dynasty  of  the  Ptolemies  in  Egypt,  and  to  that  of 
the  Seleucidce  in  Syria  (founded  by  two  of  his  generals), 
and  so  the  Greek  language  and  Greek  culture  became 
spread  over  all  the  most  civilised  and  important  part 
of  the  then  known  world.  At  that  time,  Rome  was 
only  contending  for  dominion  over  adjacent  Italian 
territories,  and  the  Greek  cities  of  South  Italy  still 
flourished  in  security  and  independence.  Indeed, 
Greek  influence  and  culture  become  more  than  ever 
diffused  around  the  Mediterranean  and  notably  in 
Western  Asia, 


HISTORY 


321 


I 


322  ELEMENTS   OF   SCIENCE 

But  Greece  itself  and  Macedonia  (now  reckoned  a 
part  of  it)  fell  into  great  confusion,  the  Macedonian  royal 
family  became  extinct,  and  the  crown  passed  to  one  of 
Alexander's  generals,  while  another,  Antipatros,  con- 
quered Athens  B.C.  322.  Epirus,  however,  rose  into 
importance  under  King  Pyrrhus,  who  died  B.C.  272. 
The  days  of  single  city  rule  were  now  over,  and,  except 
Sparta  on  the  south  and  Macedonia  on  the  north, 
Greece  was  divided  into  small  States,  each  consisting 
of  confederated  cities  and  territories. 

But  all  internecine  disputes  were  ere  long  put  an 
end  to  by  the  growing  power  of  Rome.  Four  Macedo- 
nian wars  took  place  and  ultimately  (B.C.  146)  Greece 
was  practically  subdued,  though  Athens  and  several 
other  Greek  cities  and  islands  retained  for  a  time  a 
nominal  independence. 

Since,  as  we  have  already  said,  the  civilisation  of  the 
ancient  Roman  Empire  is  still  being  directly  carried 
down  and  furthered  by  ourselves,  the  artistic,  philoso- 
phic and  religious  conditions  of  Greece  are  most  im- 
portant matters  for  consideration,  as  they  so  directly  and 
powerfully  influenced  that  ancient  Roman  civilisation. 

The  perfection  of  the  plastic  art  in  Greece,  with  which 
the  names  of  Phidias  and  Praxiteles  are  associated,  is 
revealed  to  us  by  many  precious  sculptured  relics,  while 
the  ruins  of  the  great  Athenian  temple  of  the  city's 
patron  goddess,  Athene,  with  many  others  of  less  re- 
nown, proclaim  the  skill  and  refinement  of  Grecian 
architecture.  Homer  and  the  dramatists  have  been 
already  mentioned,  while,  as  historians,  we  may  name 
Xenophon,  Herodotus,  and,  above  all,  Thucydides,  who, 
in  his  history  of  the  Peloponnesian  war,  set  a  model  for 
all  time  of  historical  description  and  narrative.  The 
same,  perhaps,  may  be  affirmed,  as  regards  oratory,  of 


HISTORY  323 

Demosthenes ;  but  for  an  account  of  Greek  art  and 
literature  the  reader  must  have  recourse  to  special 
treatises.  The  reader  should  also  seek  elsewhere  for 
a  description  of  Greek  religion  and  philosophy,  though 
a  few  words  on  each  of  these  subjects  must  here  be 
said. 

The  religion  of  a  very  large  part  indeed  of  the  human 
race  has  had  its  origin  in  the  propitiation  and  worship 
of  deified  ancestors,  though  such  marvellous  natural 
objects  as  the  sun,  moon,  and  stars,  doubtless  in  many 
instances  received  a  self-suggested  worship.  Animals 
with  their  wonderful  instincts,  especially  when  taken  in 
connection  with  human  ancestors  named  after  them, 
have  been  widely  venerated,  notably  in  Egypt,  where 
bulls  and  crocodiles,  cats  and  other  animals,  received 
divine  honours  in  different  localities.  Even  plants  have 
not  been  altogether  neglected,  and,  indeed,  amidst  tribes 
dwelling  in  almost  treeless  plains,  such  an  object  as  a 
tree,  self  sustaining  and  spreading  abroad  on  all  sides 
vast  arms  which  give  rise  to,  shed  and  renew,  a  multi- 
tude of  leaves,  may  well  seem  the  expression  of  some 
mysterious  divine  energy  within  it. 

But  the  Greeks,  with  all  the  other  divisions  of  the 
great  Aryan  family  of  nations,  reverenced  various 
powers  of  Nature  as  distinct  divinities,  whose  names  in 
different  languages  are  akin.  Thus,  that  of  the  old 
English  god  Tue  (whence  Tuesday)  resembles  Zeus,  the 
great  "  cloud-compelling "  god  of  the  sky.  The  special 
god  of  the  Greeks  was  indeed  the  sun,  revered  and 
worshipped  as  Apollo,  who  had,  at  Delphi,  a  world- 
renowned  temple.  The  moon,  the  sun,  and  the  dawn, 
had  each  their  divine  representatives ;  but  such  objects 
did  not  suffice  to  satisfy  the  Greek  religious  feeling. 
The  actions  of  men,  their  passions  and  desires,  were  also 


324  ELEMENTS   OF   SCIENCE 

deified,  as  in  Ares,  the  god  of  war,  in  Aphrodite,  of 
love,  and  in  the  god  of  wine,  Dionysios. 

But  the  Greek  religion,  like  that  of  so  many  other 
nations,  was  especially  a  religion  of  cities,  and,  indeed, 
was  of  the  essence  of  the  city.  For  a  city  may  be  said  to 
have  been  a  collection  of  men  adoring  the  same  god  by 
rites  which  were  deemed  effective  for  securing  the  exclu- 
sive or  predominant  aid  and  protection  of  the  power  so 
worshipped.  Hence,  to  neglect  the  due  worship  of  such 
a  supernatural  patron,  was  to  be  unfaithful  to  the 
interests  of  the  city,  and  even  to  be  more  or  less  of  a 
traitor.  Any  recognition  of  such  a  thing  as  a  "  right  of 
conscience"  justifying  a  dissent  from  established  prac- 
tice was  impossible.  It  could  not,  indeed,  well  have 
been  even  conceived  of. 

Worship  was  made  up  of  prayers,  processions  and 
mystic  movements,  the  sacrifice  of  animals,  and  offerings 
of  food,  and  various  more  or  less  precious  objects,  with 
incense,  music,  and  song.  But  religion  consisted  in  such 
acts  themselves,  and  not  at  all  in  morality,  save  in  so 
far  as  it  was  "  moral "  to  do  what  was  serviceable  to  the 
State.  To  do  what  had  to  be  done,  not  for  the  pleasure 
of  doing  it,  but  because  it  was  a  thing  religion  demanded, 
had  necessarily  to  some  extent  a  moral  character,  even 
though  the  action  in  itself  might  have  been  an  immoral 
one. 

But  the  morality  of  Greece  was  exceedingly  different 
from  our  own,  above  all  as  regards  the  relations  of  the 
sexes.  This  was  doubtless  in  part  the  effect,  and  in  part 
the  cause,  of  the  great  multitude  of  fantastic  and  often 
gross  fables  which  were  related  and  believed  concerning 
the  actions  of  the  gods  worshipped.  The  Greek  religion 
was  not  a  religion  of  definite  dogma,  but  of  recognised 
ritual  practices,  and  it  did  not  profess  to  give  any 


HISTORY  325 

revealed  account  of  the  origin  and  essential  nature  of 
the  beautiful  world  which  Grecian  eyes  beheld. 

Such  explanations  of  Nature,  as  well  as  the  inculcation 
of  moral  doctrines,  belonged  not  to  religion  but  to 
philosophy.  Philosophy,  after  having  studied  the  world, 
the  nature  of  man  and  his  duties,  also  occupied  itself 
with  attempts  to  penetrate  divine  things,  the  meanings 
of  the  popular  tales  concerning  the  gods,  and  the  nature 
and  attributes  of  the  Supreme  Being. 

As  to  the  explanations  of  the  world  wrhich  philosophy 
suggested,  Thales,  a  man  of  Phrenician  descent,  born 
about  640  B.C.,  taught  that  water  is  the  original  source 
of  all  things ;  Anaximander,  of  Miletus  (6 1 1  B.C.),  affirmed 
that  the  principle  of  all  things  is  an  undefined  matter, 
at  once  the  source  of  what  he  deemed  the  elementary 
contraries — namely  the  warm,  the  cold,  the  moist  and 
the  dry.  The  earth,  he  said,  arose  from  fluid,  and  all 
animals  were  at  first  aquatic.  But  he  appears  to  have 
held  that  man  has  a  soul  of  the  nature  of  air. 

Pythagoras  (529  B.C.)  founded  a  very  influential 
society,  and  instituted  numerous  ethical  regulations.  He 
taught  *  that  "  number  "  was  the  principle  underlying 
all  things — in  the  word  "  one "  is  the  beginning  of 
them  all. 

Anaximenes,  of  Miletus  (about  528  B.C.),  represented  an- 
as the  first  principle,  and  fire,  wind,  clouds,  water  and 
earth,  as  having  been  thence  produced  by  condensation. 

Diogenes,  of  Apollonia,  a  contemporary  of  Pytha- 
goras, followed  Anaximenes  in  holding  air  to  be  the 
origin  of  things,  but  believed  such  air  to  be  vital  and 
intelligent,  like  the  human  soul. 

Xenophanes   (569    B.C.)   taught   that    "the   one"   of 

*  See  ante,  p.  5. 


326  ELEMENTS   OF   SCIENCE 

Pythagoras  must  be  one  infinite  self-existing  intel- 
ligence. 

Heraclitus,  of  Ephesus,  identified  the  Supreme  Divine 
Spirit  with  an  ethereal  fire,  and  affirmed  that  all  things 
are  in  a  flux  and  a  perpetual  "  becoming." 

Parmenides  (515  B.C.),  on  the  contrary,  following 
Xenophanes,  inculcated  the  necessary  existence  of  "  the 
one."  He  said  that  it  alone  existed  and  was  everything, 
and  that  plurality  and  change  were  but  empty  appear- 
ances— mere  deceptions  of  the  senses  obscuring  the 
unchanging  unity  perceptible  to  thought. 

ZenOj  of  Elea  (who  taught  Pericles  and  was  born  about 
485  or  490  B.C.),  defended  the  doctrine  of  Parmenides, 
and  denied  the  reality  and  possibility  of  motion,  on 
the  ground  of  four  arguments,  which  readers  will  find 
described  in  histories  of  philosophy. 

Anaxagoras  (born  about  500  B.C.)  reduced  all  origin 
and  decay  to  a  process  of  mingling  and  separation,  but 
assumed,  as  ultimate  elements,  an  unlimited  number  of 
primitive  determinate  substances.  They  first  existed 
mixed  together,  and  then  the  divine  mind,  out  of  such 
chaos,  formed  the  world. 

Empedocles  (of  the  same  period)  affirmed  the  existence 
of  but  four  elements :  earth,  water,  air,  and  fire,  with 
love  as  a  uniting,  and  hate  as  a  separating  force. 

Democritus  (born  460  B.C.)  advocated  the  celebrated 
doctrine  of  atoms,  declaring  such  atoms  to  be  the  in- 
visible, intangible,  primary  elements  which  compose  all 
things  according  to  their  different  modes  of  combination 
and  relative  position. 

The  foregoing  enumeration  must  suffice  as  a  catalogue 
of  the  names  of  the  principal  philosophers  of  the  first 
period  of  Grecian  philosophy.  Its  second  period  is  less 
directly  concerned  about  the  material  universe,  and 


HISTORY  327 

deals  by  preference  with  man  as  a  thinking  being,  his 
duties  and  his  thoughts — that  is,  Ethics  and  Logic. 

Certain  teachers,  of  whom  Protagoras,  of  Abdera 
(about  490  B.C.),  is  a  type,  accepting  and  applying  the 
doctrine  of  Heraclitus  "that  all  things  are  in  a  per- 
petual flux,"  asserted  man  to  be  the  measure  of  all 
things,  and  that  just  as  each  thing  appears  to  each  man, 
so  is  it  for  him.  Thus  all  things  are,  he  taught,  but 
relative;  everything  is  uncertain  in  reality,  even  the 
existence  of  the  "Immortal  Gods."  What  applies  to 
our  perception  of  things,  also  applies  to  our  perception 
of  their  relations,  and  thus  all  morality  becomes  under- 
mined, because  nothing  can  be  certainly  affirmed  to 
be  good  save  as  it  may  appear  to  be  good  in  the  e}^es 
of  those  who  so  regard  it.  Nevertheless  .this  very 
moral  revolt  was  an  indirect  assertion  of  the  rights  of 
conscience ;  for  since  that  was  certain  to  each  man  which 
seemed  to  him  so  to  be,  he  had  a  justification  for  refus- 
ing to  comply  with  behests  he  deemed  wrong,  and  for 
denying  the  ethical  validity  of  commands  on  the  part  of 
the  State.  Such  teachers  (since  they  were  by  profession 
instructors  in  eloquence  and  polite  learning)  were  termed 
Sophists.  In  the  teaching  of  later  members  of  that  school 
the  evil  consequences  which  attended  their  teaching 
became  more  conspicuous ;  as,  e.g.,  in  Thrasymachus,  who 
identified  "right"  with  the  personal  interest  of  a  man 
in  power.  A  reaction  against  such  doctrines  was  inevit- 
able, and  it  came  to  a  head  in  that  immortal  teacher 
Socrates,  who  was  born  about  470  B.C.  His  supreme 
claim  to  distinction  and  reverence  consists  in  his  having 
ta aght  that  virtue  does  not  consist  in  acts  but  in  inten- 
tions. He  distinguished  between  merely  external  virtue 
and  its  true  essence,  which  he  affirmed  to  be  absolutely 
dependent  on  moral  perceptions.  As  our  readers  know, 


328  ELEMENTS   OF   SCIENCE 

he  was  fatally  misunderstood  and  condemned  to  die  for 
not  recognising  the  gods  which  the  State  recognised. 
Yet  he  was  a  devout  man,  and  while  dying  from  the  cup 
of  hemlock  given  him,  reminded  a  friend  that  they 
owed  the  offering  of  a  cock  to  the  god  Esculapius.  His 
martyrdom  for  the  cause  of  philosophic  morality  gave  a 
wide-spread  and  most  enduring  influence  to  his  teaching. 
In  the  Socratic  principle,  that  virtue  depends  on  know- 
ledge, much  of  the  future  course  of  philosophy  was 
indicated — namely,  an  examination  of  ethics  on  the  one 
hand  and  of  reasoning  on  the  other. 

Euclid  of  Megara  (not  the  geometrician),  being  imbued 
with  the  notion  of  the  school  of  Parmenides,  that  "  the 
one"  is  everything,  taught  that  "the  one"  is  really 
"  the  good."  He  and  his  followers  devoted  themselves 
to  that  side  of  the  Socratic  teaching  which  concerned 
reasoning. 

Antisthenes  (born  444  B.C.)  and  his  disciples  devoted 
themselves  to  its  ethical  and  practical  side,  which  he 
morbidly  exaggerated.  But  he  appears  to  have  affirmed 
the  unity  of  God,  despising  the  popular  beliefs.  From  the 
place,  named  Cynosarges,  where  he  met  his  followers, 
they  acquired  the  surname  of  Cynics,  of  whom  Diogenes 
has  become  the  accepted  type.  He  proclaimed  the  need 
not  only  of  renouncing  the  luxuries  but  even  the 
decencies  of  life,  and  adopted  an  ostentatious  asceticism 
which  in  some  of  his  followers  became  brutal  and 
indecent. 

Aristippus  of  Gyrene,  a  disciple  of  Socrates,  laid  stress 
above  all  on  the  exercise  of  the  will  according  to  reason. 
The  Cynics  sought  for  independence  through  the  renun- 
ciation of  enjoyment;  but  Aristippus  advocated  self- 
control  in  enjoyment,  by  which  true  pleasure  was  to  be 
attained.  That  such  is  the  real  end  of  life  and  the  test 


HISTORY  329 

of  truth  was  taught  by  him  and  hie  followers,  who  con- 
stituted the  Cyrenaic  school. 

In  Plato  (from  427  B.C.)  the  diverse  tendencies  of  the 
Socratic  teaching  were  combined  into  a  system.  The 
highest  good,  he  taught,  to  be  neither  pleasure  nor  know- 
ledge, but  the  greatest  possible  likeness  to  God  as  the 
absolutely  good. 

Of  his  method,  his  theory  of  "  ideas,"  his  psychology 
and  theology,  nothing  can  here  be  said,  except  that  his 
conceptions  were  in  many  respects  so  lofty,  refined,  and 
admirable,  as  to  have  largely  been  made  use  of  by  most 
esteemed  Christian  teachers  at  different  times  in  later  ages. 

The  same  was  the  case  to  a  still  further  extent  with 
respect  to  Aristotle  (born  384  B.C.),  the  tutor  of  Alex- 
ander the  Great.  He  was  perhaps  the  most  wonderful 
genius  the  world  has  ever  seen — his  mental  activity 
was  so  acute,  profound,  and  manifold.  His  treatises  not 
only  on  philosophy  but  also  on  ethics,  politics,  physics, 
psychology,  and  various  other  subjects,  are  all  in  various 
respects  admirable.  To  him  we  also  owe  the  science 
of  logic,  while  he  was  the  father  of  biological  science, 
and  many  of  his  descriptions  of  animal  anatomy  are 
amazingly  accurate. 

Pyrrho  (from  about  360  to  270  B.C.)  was  the  founder 
of  the  philosphical  sect  known  as  the  Sceptics.  His 
scepticism  was  so  great  as  to  include  scepticism  of 
his  own  system,  and  he  declined  to  enunciate  any 
affirmation.  He  and  his  school  said:  "We  assert 
nothing,  not  even  that  we  assert  nothing."  Thus  it 
was  necessarily  impossible  for  them  logically  to  even 
attempt  to  sustain  their  own  cause. 

As  we  have  seen,  the  Cyrenaics  affirmed  that  the 
greatest  good  was  happiness.  This  was  translated  by 
Epicurus  (341-270  B.C.)  into  pleasure — the  sole  good 


330  ELEMENTS   OF  SCIENCE 

and  true  end  in  life  to  his  followers,  the  Epicurean,  who 
taught  that  the  gods  were  also  divinely  happy,  and 
never  deigned  to  occupy  themselves  about  human  actions 
and  affairs. 

The  greatest  contrast  to  the  Epicureans  were  the 
Stoics,  a  philosophic  sect,  which  arose  out  of  the  school 
of  the  Cynics,  being  a  refined  and  elevated  modification 
thereof.  Their  founder,  Zeno  of  Cyprus,  alarmed  at  the 
spread  of  scepticism,  taught  publicly  (about  308  B.C.) 
that  the  aim  of  man's  existence  is  neither  to  be  wise 
nor  to  enjoy,  but  to  be  virtuous,  to  which  end  both 
knowledge  and  pleasure  are  to  be  employed  as  means, 
while  being  kept  strictly  subordinate.  The  aim  set 
forth  was  an  eminently  practical  one — to  become  a 
"  perfect  man."  Zeno  was  succeeded  in  turn  by 
Cleanthes  and  Chrysippus  (282-209  B.C.). 

Meantime  a  fresh  development  of  scepticism — called 
the  New  Academy — took  place.  It  was  promoted  by 
Arcesilaus  (315— 241  B.C.)  and  later  by  Carneades  (214- 
129  B.C.).  This  school  did  not  adopt  the  absurd,  self- 
contradictory  scepticism  of  Pyrrho.  It  did  not  profess  to 
deny  that  we  can  affirm  anything  with  certainty,  but  only 
that  we  can  so  affirm  nothing  except  appearances  and 
our  own  feelings.  Thus  it  admitted  a  certain  kind  of 
knowledge,  but  denied  we  could  know  anything  other- 
wise than  as  related  to  ourselves  and  to  other  things.  It 
was  a  doctrine  affirming  "  the  relativity  of  knowledge," 
and  logically  resulted  in  more  uncertainty  and  scepticism 
than  its  upholders  themselves  admitted.  Such  were  the 
main  features  of  Greek  philosophy  in  Greece. 

But  Grecian  Egypt,  at  Alexandria,  developed  yet  a 
third  school  of  philosophy,  known  as  Neo-platonism.  It 
was  essentially  religious,  and  was  largely  influenced  by  the 
speculations  of  certain  Jewish  thinkers  who  had  imbibed 


HISTORY  331 

Hellenic  culture.  But  what  it  may  be  needful  to  remark 
about  it  must  be  deferred  till  we  have  noted  various  facts 
about  those  who  so  influenced  it,  and  therefore  we  must 
now  leave  the  Greeks  and  direct  our  attention  to  the 
Hebrews. 

The  Jews  'were  a  relatively  small  Semitic*  people 
whose  influence  on  the  world  has  been  even  more 
profound  and  important  than  that  of  the  Greeks, 
because  it  has  affected  not  science,  literature  and  art,  but 
morals  and  religion.  Very  little  need  be  said  about  their 
history  in  a  work  addressed  to  English-speaking  people 
who  are  so  familiar  with  the  Bible.  Much  would  have  to 
be  said,  however,  if  there  was  here  any  need  to  consider 
and  weigh  questions  which  modern  Biblical  criticism 
has  made  matters  of  controversy ;  but  in  dealing  with 
the  mere  elements  of  history  it  will  be  enough  simply  to 
refer  to  them. 

When  the  reputed  descendants  of  Abraham  began  and 
completed  the  conquest  of  Canaan,  sacrifices  were  offered 
in  various  parts  of  the  land,  and  by  men  who  were  not 
priests,  as  we  read  in  the  Books  of  Judges,  Samuel,  and 
Kings.  Nevertheless  they  were  worshippers  of  one  God, 
Jehovah — whether  or  not  he  was  regarded  as  more  than 
a  tribal  deity  who  watched  over  the  Jewish  nation,  as 
other  nations  were  watched  over  and  protected  by  their 
various  gods.  The  prophets,  Amos,  Hosea,  Isaiah,  and 
Micah  most  probably  date  from  before  623  B.C.  They, 
and  indeed  all  the  prophets,  defended  the  exclusive 
worship  of  Jehovah,  insisted  on  his  moral  character,  and 
proclaimed  morality  to  be  not  only  absolutely  necessary, 
but  that  it  is  the  chief  element  of  all  true  worship. 

In  the  separate  Northern  portion  of  the  nation  (Israel) 

*  See  ante,  p.  317. 


332  ELEMENTS   OF   SCIENCE 

Amos  prophesied  under  its  second  king,  Jeroboani,  who 
died  743  B.C.  The  end  of  the  conflict  of  Israel  with 
Syria  was,  as  the  reader  knows,  the  Captivity  (725  B.C.) 
and  loss  of  the  Ten  Tribes.  By  this  loss  the  Southern 
nation  (Judah)  had  its  sentiments  of  patriotism  and  racial 
distinctness  accentuated.  A  further  concentration  and 
intensification  of  the  Jewish  nationality  was  effected  by 
the  reform  of  King  Josiah  (623  B.C.),  who  promulgated 
the  Book  of  Deuteronomy,  whereby  all  sacrifice  was  limited 
to  the  temple  of  Jerusalem  and  a  Levitical  priesthood. 
This  was  at  the  beginning  of  the  period  of  the  conflict  of 
the  Jews  with  Babylon,  which  ended  in  the  captivity  of 
Judah,  under  Nebuchadnezzar  (597-566  B.C.),  a  little 
before  which  were  the  writings  of  Jeremiah  and 
Zephaniah,  whose  whole  spirit  is  in  complete  accord  with 
Deuteronomy.  But  with  the  captivity  and  consequent 
loss  of  independent  nationality,  the  religion  of  the  Jews 
was  yet  further  intensified.  The  "nation"  became 
more  or  less  changed  into  an  "  hereditary  Church,"  while 
the  stream  of  prophecy  began  to  flow  in  the  direction  of 
ritual  observance,  and  was  not,  as  before,  almost  entirely 
ethical.  Thus  the  full  development  of  Judaism  was 
carried  much  further  during  the  exile  by  Ezekiel,  who 
was  himself  a  priest  and  for  years  an  official  at  Jerusalem. 
He  commanded,  in  the  name  of  Jehovah,  that  a  distinc- 
tion should  be  made  between  priests  and  Levites,  the 
former  alone  being  permitted  to  sacrifice.  Divine  re- 
wards and  punishment  for  the  individual  came  to  the 
front  in  place  of  the  older  notion  which  regarded  the 
community  almost  exclusively.  Instead  of  what  was  said 
by  the  old  prophets  :  "  Let  Israel  love  justice,  and  Jehovah 
will  reward  the  nation  accordingly,"  Ezekiel  taught : 
"Let  the  individual  love  justice,  and  Jehovah  will  reward 
him." 


HISTORY  333 

After  seventy  years  captivity,  Cyrus,  having  conquered 
Babylon,  permitted  many  of  the  Jews  to  return  (536  B.C.), 
under  Zerubbabel,  and  they  began  to  rebuild  the  temple. 
Under  Darius  (520  B.C.) — the  period  of  Haggai  and 
Zechariah — and  under  Ezra  and  Nehemiah  (456  B.C.), 
of  whom  Malachi  was  a  late  contemporary,  the  return 
from  exile  was  completed.  Then,  it  is  now  supposed,  the 
Books  of  Chronicles  were  written  and  the  Levitical  code 
completely  elaborated,  and  it  is  to  this  period  that  modern 
critics  attribute  the  Pentateuch,  which  incorporated 
many  very  ancient  fragments  of  divers  origins  and 
authorships. 

Under  the  mild  rule  of  the  Persian  kings,  the  Jews 
were  allowed  to  manage  their  internal  affairs,  and  the 
high  priest  was  their  chief  magistrate.  They  strictly 
avoided  inter-marriage  with  foreigners,  and  their  detesta- 
tion of  idolatry  became  extreme,  as  also  did  their  spirit 
of  nationality  and  attachment  to  their  peculiar  observ- 
ances. The  nation  thus  lived  peacefully,  till,  in  the  year 
333  B.C.,  Alexander  the  Great  appeared  in  Syria,  when 
Jerusalem  made  its  submission  and  was  spared.  Upon  the 
death  of  the  conqueror,  Judsea  fell  under  the  dominion 
of  the  Ptolemies,  who  favoured  the  Jews,  and  planted  a 
colony  of  them  in  Alexandria  wh:ch  had  much  influence 
on  the  intellectual  and  religious  future  of  the  world,  as  we 
shall  see.  But  a  general  named  Antiochus,  who  accom- 
panied Alexander  to  the  East,  had  a  son  Seleucus,  who 
ultimately  obtained  the  sovereignty  of  Syria,  raised  the  city 
of  Antioch  and  founded  a  dynasty — that  of  the  Seleucida?.* 
Their  kingdom  extended  at  first  over  the  eastern  part  of 
Asia  Minor,  and  thence  to  beyond  the  Indus.  About 
256  B.C.,  however,  a  people  of  Northern  Persia — the 


*  See  ante,  p.  320. 


334  ELEMENTS   OF   SCIENCE 

Parthians — revolted  and  established  a  powerful  kingdom 
between  the  Caspian  and  the  Persian  Gulf.  Under  the 
Ptolemies  and  Seleucidse,  Greek  influence  gained  much 
ground  even  amongst  the  Jews,  while,  as  before  said,*  it 
then  extended  far  and  wide  around  the  Mediterranean. 
Judaea  passed  under  the  sway  of  the  Seleucidse  during  the 
reign  of  Antiochus  the  Great — 198  B.C.  He  visited 
Jerusalem,  confirmed  its  privileges,  and  by  his  benignity 
still  further  promoted  the  influence  of  Hellenic  culture 
over  the  Jews.  But  the  increase  of  that  influence  greatly 
augmented  the  national  and  religious  passions  of  such 
of  the  Jews  as  did  not  yield  to  it,  so  that  a  strong 
antagonism  was  produced  between  these  two  sections  of 
that  nation. 

In  the  reign  of  his  second  son,  Antiochus  Epiphanes,  a 
great  change  took  place.  He  determined  to  force  the 
Jews  to  renounce  Jehovah  and  worship  the  Roman  god 
Jupiter.  Intrigues  to  obtain  the  post  of  high  priest 
and  consequent  disorders,  for  a  time  favoured  his  attempt, 
and,  after  great  slaughter,  the  Jewish  worship  was 
abolished  and  sacrifices  to  Jupiter  were  offered  before 
his  image  in  the  temple  of  Jerusalem.  This  gave  rise 
to  the  well-known  rising  of  the  Maccabees,  which,  after 
an  alliance  with  Home,  succeeded.  Ultimately  the 
Maccabee  Jonathan  became  king  of  the  Jews,  and 
founded  a  dynasty — that  of  the  Asmonceans — which 
lasted  for  about  a  century  till  the  last  of  the  dynasty 
was  killed  by  Herod  the  Great,  who,  with  the  support  of 
the  Romans,  became  king  of  Judaea  38  B.C.,  which  at  his 
death  became  a  district  of  the  Roman  province  of  Syria. 
A  succession  of  exceptionally  rapacious  Roman  governors 
led  to  the  terrible  revolt  which  ended  in  the  total 

*  gee  ante,  p.  320. 


HISTORY  335 

destruction  of  Jerusalem,  70  A.D.  One  more  struggle 
produced  a  further  desolation  of  Judaea  by  the  Emperor 
Hadrian,  who  issued  an  edict  forbidding  circumcision, 
the  reading  the  Mosaic  law  (the  Pentateuch),  and  the 
observance  of  the  Sabbath. 

Then  the  dispersion  of  the  Jews  over  the  world  became 
greatly  augmented.  It  had  indeed  begun  much  earlier, 
under  the  Ptolemies,  and  was,  as  before  said,  promoted 
by  Antiochus  the  Great,  who  settled  large  numbers  in 
various  Asiatic  cities.  In  the  time  of  Cicero  there  was 
already  a  wealthy  community  of  Jews  in  Italy.  After 
Hadrian,  the  Jews  spread  throughout  the  Empire  were 
allowed  to  follow  their  old  usages  and  rites,  and  new 
synagogues  and  schools  were  erected  in  e,ll  directions. 
But  they  strictly  maintained  their  racial  distinctness 
and  remained  a  people  apart  and  by  themselves,  in  a 
way  quite  different  from  any  other  people— Egyp- 
tians, Greeks,  or  Gauls  —  which  had  their  several 
representatives  in  various  parts  of  the  Empire.  This 
fact  is  very  characteristic  of  the  Hebrews,  but 
most  important  of  all  is  their  strict  monotheism  and 
their  detestation  of  idolatry,  whereby  they  had  come  to 
differ  so  exceedingly  from  all  other  nations  of  that  period 
of  the  world's  history,  and  most  notably  from  their 
brother  Semites,  the  Pho3nicians  of  Syria,  and  the 
Carthagenians.  Part  of  their  spirit  of  nationality  was 
due  to,  as  it  was  intensified  by,  the  various  prophecies 
which  had  led  them  to  expect  (though  they  rejected)  the 
Messiah,  and  which  had  caused  various  impostors  or  en- 
thusiasts to  assume  to  themselves  that  character  during 
the  century  which  preceded  the  destruction  of  Jerusalem. 

The  Jews  had  done  nothing  to  advance  either  science 
or  art,  and  did  not  do  so  for  centuries,  nor  till  they 
came  closely  in  contact  with  the  Greeks  at  Alexandria, 


336  ELEMENTS   OF   SCIENCE 

did  they  influence  the  course  of  philosophic  thought. 
Their  great  characteristic  was  their  religion  and  the 
lofty  moral  precepts  which  were  closely  interwoven 
therewith.  In  spite  of  a  tendency  slavishly  to  adhere 
to  minute  ceremonial  observances,  their  moral  atmo- 
sphere was  a  healthy  one  indeed  compared  with  that  of 
the  Greeks.  Their  ethical  precepts  were  not  confined  to 
speculative  exceptional  minds — the  disciples  of  some 
philosophic  school — but  were  disseminated  far  and  wide 
throughout  all  classes  of  the  people.  In  their  firm 
determination  rather  to  undergo  persecution  than  violate 
their  conscience  as  regards  their  religious  duties,  the 
Jews  set  a  great  and  novel  example  to  the  world.  Many 
were  the  martyrs  who  thus  suffered  under  Antiochus 
Epiphanes  and  subsequently  under  the  Roman  emperors. 
Torture  and  death  were  not  seldom  their  portion  as  a 
consequence  of  their  refusal  to  perform  what  in  their 
eyes  were  acts  of  detestable  idolatry. 

In  speaking  of  the  Jews  it  has  been  necessary  to  refer 
to  the  Romans.  We  will  conclude  this  chapter  with  an 
elementary  notice  of  Roman  history,  which  will  bring  us 
to  the  dawn  of  the  modern  world,  and  enable  us  to  see 
those  factors  from  the  interaction  of  which  our  present 
civilisation  has  arisen  as  a  necessary  consequence. 

The  Aryans  who  entered  the  peninsula  of  Italy, 
found  it  already  inhabited,  probably  by  a  race  akin  to 
the  existing  Basques.  The  first  Aryan  swarm  seem  to 
have  been  the  Celts,  who,  besides  appropriating  what  is 
now  France  and  the  British  Isles,  occupied  all  the  north 
of  Italy  down  to  where  now  stand  Milan  and  Bologna. 
This  latter  was  known  as  Cisalpine  Gaul,  the  Celtic 
continental  dominion  north  of  the  Alps  constituting 
Transalpine  Gaul. 

The  Teutons  (the  ancestors  of  the  English,  the  Germans, 


HISTORY  337 

and  the  Scandinavians)  and  the  Slavs  (the  ancestors  of 
the  earliest  Prussians,  the  Poles,  Russians,  and  Bohemians) 
were  the  two  great  swarms  of  Aryans  who  established 
themselves  in  Europe. 

Italy  at  and  near  the  coast,  from  the  Po  to  what  is 
now  Genoa,  and  thence  for  a  space  westward,  was  the 
province  of  the  Ligurians,  while  a  more  or  less  closely 
allied  race  peopled  the  islands  of  Corsica  and  Sardinia, 
with  part  of  Sicily.  The  migrations,  or  invasions,  which 
introduced  what,  in  a  restricted  sense,  are  to  be  called 
Italians,  have  not  yet  been  ascertained.  Another  people 
(settled  in  Italy  before  the  dawn  of  history)  were 
the  Etruscans — renowned  for  their  cities,  constructed  of 
large  stones,  and  their  superstitions.  History  discovers 
them  with  a  thriving  domain  still  extending  over  the 
Eastern  half  of  Italy  from  the  Arno  to  the  Tiber. 
Around  quite  the  south  of  Italy  were  a  number  of  Greek 
colonies,  some  of  which  so  much  extended  and  prospered 
as  to  cause  that  part  of  Italy  to  be  distinguished  from 
what  was  the  mother  country  of  its  inhabitants,  as 
Gh'eat  Greece.  The  rest  of  Italy — between  Etruria, 
Cisalpine  Gaul  and  Magna  Graecia — was  inhabited  by 
the  Italians,  who  seem  to  have  been  a  race  more  nearly 
allied  to  the  Grecian  than  to  any  other  branch  of  the 
great  Aryan  stock.  Nevertheless  they  were  not,  111 
early  times  (like  the  Greeks),  a  seafaring  and  colonising 
people,  a  fact  probably  due  to  the  very  much  less 
indented  coast-line  of  the  country  they  inhabited.  The 
Italians  consisted  of  various  tribes,  whereof,  from  the 
west  coast  inwards,  the  north  was  inhabited  by  the 
Umbrians;  while  further  south  were  the  Apulians,  east 
of  which  were  the  Samnites,  who  reached  down  towards 
the  Lucanians — the  neighbours  of  the  Italian  Greeks. 
Between  the  Umbrians  and  what  ultimately  became 


338  ELEMENTS   OF  SCIENCE 

Rome,  were  the  Sabines,  south  and  south-east  of  these 
were  the  Latins  and  the  Volscians,  while  between  the 
Latins  and  the  Umbrians  were  the  ^quians. 

The  origin  of  Rome  is  still  unknown,  as  is  the  history 
of  its  early  kings.  Situated  on  the  Tiber,  which  was 
the  south  Etrurian  boundary,  it  was  probably  erected 
as  a  bulwark  of  the  Latins  to  defend  them  from  the 
Etrurians.  It  was  built  on  a  hill  known  as  the 
Palatine,  where  was  a  settlement  of  the  Latin  tribe 
called  Ramnes  or  Romans.  Another  settlement,  on  the 
Capitoline  hill,  was  made  by  the  Sabines,  and  a  league 
was  established  between  the  two ;  so  that  they  formed 
one  city  with  two  sets  of  inhabitants — the  Sabines 
becoming  reckoned  as  citizens  of  the  first  settlement  and 
therefore  "  Romans "  also.  Their  kings  were  not 
hereditary,  and  the  last  of  them,  the  Tarquins,  have 
been  thought  to  have  been  of  Etruscan  origin.  They 
much  adorned  Rome,  and  made  it  the  most  powerful  of 
the  Latin  cities.  The  monarchical  constitution  is  not 
precisely  known,  but  the  people  consisted  of  two  classes — 
the  patricians,  or  nobles,  and  the  plebeians,  or  common 
people.  The  former  were  probably  descendants  of  the 
oldest  inhabitants,  and  the  latter  of  men  admitted  later 
to  the  city's  privileges.  From  these  classes  there  arose 
(i)  a  noble  assembly  or  senate,  and  (2)  a  popular 
assembly.  The  plebeians  were  full  Roman  citizens,  but 
there  was  a  gradually  increasing  mass  of  slaves  who  had 
no  rights  whatever ;  so  that  the  plebeians  formed  a  sort 
of  secondary  aristocracy  of  the  whole  population  of  the 
city.  About  510  B.C.  the  monarchy  was  put  an  end  to 
through  the  king  Lucius  Tarquinius — called  Superbus, 
or  proud — being,  with  his  family,  expelled  from  Rome. 
A  highly  aristocratic  republic  was  then  established,  with 
the  senate  and  popular  assembly  as  before,  but  also  with 


HISTORY  33§ 

two  annually  elected  magistrates,  called  consuls,  at  the 
head  of  the  State. 

Thereafter  great  dissension  arose  between  the  plebeians 
and  the  patricians,  which  latter  had  kept  to  themselves  all 
the  important  offices  of  the  State  and  were  very  oppressive. 
About  460  B.C.  the  people  obtained  the  appointment  of 
two  officers,  termed  tribunes,  whose  office  was  to  protect 
the  plebeians  against  the  patricians.  But  space  cannot 
here  be  afforded  for  describing  the  Roman  State  and  its 
officers,  for  a  knowledge  of  which  and  of  all  the  details 
of  later  disputes  and  dissensions,  the  student  is  referred 
to  works  on  Roman  history.  We  must  here  observe, 
however,  that  gradually  a  reconciliation  was  effected, 
and  a  consul,  Lucius  Sextus,  was  elected  from  the 
plebeians,  366  B.C.  Before  then,  Rome  had  to  struggle 
with  her  near  neighbours  the  Etruscans,  the  ^Equians, 
and  the  Volscians,  fortifying  herself  by  effecting  a  close 
alliance  with  the  other  Latin  cities  united  together  in  a 
league.  In  time  of  danger,  a  special  officer,  called  a 
dictator,  was  chosen,  to  whom  great  power  was  accorded 
for  six  months.  Such  a  dictator  was  Marcus  Furius 
Camillus,  who  (396  B.C.)  captured  the  nearest  Etrurian 
city  (Veii)  and  greatly  extended  the  Roman  power.  Six 
years  later,  however,  they  suffered  from  an  invasion  of 
the  Cisalpine  Gauls,  who  even  captured  the  city,  though 
it  was  soon  again  liberated.  This  was  but  one  of 
several  Gaulish  inroads,  while  wars  went  on  with  sur- 
rounding tribes  which  ended  in  a  repeated  small  increase 
of  Roman  territory — their  conquered  inhabitants  being 
admitted  to  the  privileges  of  Roman  citizenship. 

More  serious  wars,  for  the  subjugation  of  all  Italy  to 
the  city  of  Rome,  then  followed — wars  with  the  Latins 
themselves,  the  Samnites,  and  others — till  (by  282  B.C.) 
Rome  had  subdued  almost  all  Italy,  save  some  of  the 


340  ELEMENTS   OF   SCIENCE 

cities  of  what  had  been  Magna  Grcecia.  The  populations 
thus  subdued  were  divided  into  three  categories,  (i) 
Those  to  whom  the  great  privilege  of  Roman  citizen- 
ship was  conceded ;  (2)  those  to  whom  a  few  municipal 
privileges  in  connection  with  the  Government  of  Rome 
were  granted.  Such  were  first  bestowed  upon  the  Latin 
cities,  on  which  account  it  has  been  termed  the  Latin 
franchise;  (3)  those  known  as  "  Italians,"  who  were 
merely  allies,  having  no  municipal  privileges  (save  their 
own  independent  ones),  but  being  bound  to  follow  the 
lead  of  Rome  in  matters  military. 

The  next  objects  of  attack  were  the  Grecian  cities  of 
the  south,  beginning  with  Tarentum,  which  applied  for 
help  to  Pyrrhus,  king  of  Epirus,  who  came  and  was 
joined  not  only  by  the  Italian  Greeks,  but 'also  by  some  of 
the  more  lately  conquered,  true  Italian  people.  After 
some  success  he  was,  however,  defeated  at  Beneventum 
(276  B.C.)  and  had  to  leave  Italy.  A  few  years  later, 
Rome  subdued  the  whole  of  Southern  Italy. 

The  time  had  now  come  for  the  powerful  and  warlike 
Roman  republic  to  enter  into  contest  with  States  alto- 
gether external  to  Italy,  and  first  with  the  neighbouring 
State  in  Africa. 

Carthage  was  a  very  wealthy,  powerful,  and  influ- 
ential city  long  before  Rome  began  to  attempt  the 
subjugation  of  Italy,  and  a  treaty  was  made  between 
the  two  cities  when  the  regal  government  of  Rome  came 
to  an  end.  Carthage  was  governed  by  a  senate  which 
does  not  seem  to  have  formed  a  close  aristocracy,  and  the 
extent  of  its  commercial  expeditions  and  conquests  no 
doubt  largely  contributed  to  greatly  develop  the  in- 
telligence of  the  community  which  peopled  what  seems 
to  have  been  a  generally  tranquil  and  well-governed 
city.  As  early  as  490  B.C.  Darius  is  said  to  have  in 


HISTORY  341 

vain  solicited  its  assistance  in  his  invasion  of  Greece.  It 
had  acquired  extensive  dominions  across  the  sea,  having 
obtained  possession  of  both  Corsica  and  Sardinia,  and  a 
large  part  of  Sicily,  long  before  Rome  had  acquired 
any  transmarine  territory.  In  the  last-named  island, 
Carthage  had  to  maintain  frequent  contests  with  the 
Greek  inhabitants,  whom  Pyrrhus  aided  during  a  certain 
interval  in  his  contest  with  Home,  before  mentioned. 

Roman  soldiers  were  Roman  citizens,  but  Carthage 
relied  mainly  on  the  aid  of  mercenary  troops  hired  in 
Spain,  and  even  in  Gaul,  as  well  as  in  Africa. 

Sicilian  disputes  involved  Rome  in  a  contest  with 
Carthage  for  the  sake  of  protecting  certain  Italians  who 
had  taken  possession  of  Mycenae.  Thus  arose  the  frst 
Punic  ivar,  which  lasted  from  264-241  B.C.,  when 
Carthage  sued  for  peace  and  yielded  up  her  Sicilian 
territories  to  Rome.  Thus  it  was  that  Rome  acquired 
her  first  foreign  dominion — her  first  province — which 
consisted  of  all  Sicily  save  what  belonged  to  Heiron,  the 
Greek  king  of  Syracuse. 

Thereafter  Rome  added  to  her  dominions  the  Cartha- 
genian  islands,  Corsica  and  Sardinia,  while  Carthage 
was  acquiring  large  dominions  in  Spain  through  the 
military  genius  of  Hannibal,  son  of  Hamilcar.  At  last 
he  took  the  city  of  Saguntum,  which  Rome  claimed  as 
her  ally,  and  so  began  the  second  Punic  war,  which  lasted 
from  218-202  B.C.  During  it,  Hannibal  made  his 
celebrated  march  across  the  Alps,  defeated  the  Romans 
at  the  battle  of  Cannae,  and  raised  several  of  Rome's 
allies  in  revolt  against  her.  But  the  Romans  meanwhile 
conquered  not  only  the  Syracuse  kingdom  in  Sicily,  but 
also  the  Spanish  dominions  of  Carthage  ;  while,  finally, 
a  naval  battle  was  gained,  under  the  Roman  commander 
Scipio,  th«  result  of  which  was  that  Carthage  had  to 


342 


ELEMENTS   OF   SCIENCE 


HISTORY  343 

give  up  all  her  African  conquests,  and  become  a  de- 
pendent ally,  bound  not  to  make  war  without  Rome's 
consent. 

Half  a  century  later,  the  sovereign  of  the  African 
kingdom  of  Numidia  (which  had  been  freed  from  the 
dominion  of  Carthage),  who  had  been  an  ally  of  Rome  in 
war,  became  at  variance  with  Carthage,  and  this  led  to 
the  third  Punic  war,  which,  after  a  struggle  of  only 
three  years,  ended  in  the  destruction  of  the  great 
African  city  (146  B.C.)  and  the  reduction  of  its  territory 
to  the  condition  of  a  Roman  province. 

Meantime,  during  the  second  Punic  war,  the  Romans 
had  begun  a  strife  which  ended  in  the  subjugation  of 
Macedonia  and  Greece,  which,  with  the  exception  of 
Athens  and  a  few  other  cities,  was  completed  at  the 
same  epoch  as  that  wherein  Carthage  was  destroyed. 
During  these  Macedonian  wars,  Antiochus  the  Great* 
crossed  the  ^Egean  Sea  (192  B.C.)  to  aid  the  Greeks, 
but  was  driven  back  by  the  Romans,  who  followed  and 
again  defeated  him.  The  result  was  that  his  dominions, 
which  had  previously  extended  from  the  ^Egean  to  far 
beyond  the  Tigris,  were  reduced  to  Syria,  with  Antioch 
for  its  capital,  the  conquered  country  being  divided 
between  Rome's  allies,  whereby  the  Romans  became  the 
real  masters  of  Western  Asia. 

The  Cisalpine  Gauls  had  greatly  aided  Hannibal  in  his 
invasion  of  Italy,  in  consequence  of  which  they  were 
likewise  subjugated  (about  191  B.C.),  as  also  Liguria  and 
the  Venetian  territory,  so  that  all  we  now  call  Italy 
became  then  subject  to  Rome. 

In  the  third  century  B.C.  Spain  was  almost  entirely 
peopled  by  Basques  (called  Iberians),  save  that  Celts 


gee  ante,  p.  334. 


344  ELEMENTS   OF   SCIENCE 

had  penetrated  to  its  centre  and  that  there  were  Greek 
and  Phoenician  colonies  on  its  coasts.  By  218  B.C., 
however,  the  southern  half  of  Spain,  with  the  Balearic 
Isles,  had  been  conquered  by  Carthage.  But  these 
conquests,  by  206  B.C.,  had  passed  to  Kome,  and  by 
130  B.C.  all  Spain  was  a  Roman  province,  save  its 
northern  mountainous  region  and  Gallicia. 

In  125  B.C.  a  Homan  province,  now  Provence,  was 
formed  in  Transalpine  Gaul  and  a  colony  founded  at 
Aix,  while  twenty  years  later  the  Roman  domain  reached 
northwards  to  Geneva  and  Toulouse.  Any  further 
advance  was  for  a  time  stopped  by  a  prodigious  invasion 
of  northern  tribes — known  as  the  Cimbri  and  Teutones — 
who  were  ultimately  routed  by  the  Consul  Marius. 

While  this  enormous  extension  of  the  power  of  the 
Roman  citizens  took  place,  there  was  at  first  no  parallel 
extension  of  their  number,  for  the  provincials  and  allies 
had  no  power  or  voice  in  the  Government,  although 
Rome  itself  was  becoming  more  democratic  by  the 
abolition  of  patrician  privileges. 

The  sovereign  power  was  in  the  hands  of  an  assembly  of 
the  people  which  passed  laws  and  elected  magistrates,  thus 
practically  electing  the  Senate,  which  mainly  consisted  of 
men  who  had  filled  office.  But  there  was  a  much  worse  dis- 
tinction than  an  aristocratic  one — that  between  rich  and 
poor — with  which  co-existed,  manhood  citizen  suffrage, 
and  thus  the  sovereign  assembly  of  the  people  became  a 
turbulent  or  venal  mob.  The  old  Roman  citizens  grew 
scarcer  from  the  slaughter  of  war,  while  strangers  who 
had  been  slaves  but  were  emancipated,  came,  asfreedmen, 
to  take  their  place.  The  dissensions  which  ensued  are 
described  in  every  history  of  Rome,  and  amongst  them 
was  the  so-called  sedition  which  ended  in  the  slaughter 
of  the  two  brothers  named  Gracchus — in  133  and  123 


HISTORY  345 

B.C.  Thereafter  Marius  (the  before-mentioned  conqueror 
of  the  Cinibri)  espoused  the  cause  of  the  poorer  classes 
and  of  the  Italians  who  desired  to  be  admitted  to  Roman 
citizenship.  Many  had  taken  up  arms  (90  B.C.)  and, 
on  their  submission,  obtained  their  desire.  The  Samnites, 
however,  would  not  submit,  and  then  Sylla — who  was 
sent  with  Marius  against  them — attained  great  credit  at 
Home,  so  that  violent  jealousy  arose  between  them, 
which  led  to  the  first  civil  war  in  Roman  history. 
Sylla  was  called  away  to  chastise  Mithridates,  king  of 
Pontus  (the  region  south  of  the  Euxine),  who  had 
massacred  Romans  and  invaded  Greece.  Sylla  stormed 
Athens,  defeated  Mithridates,  and  returned  hastily  to 
Rome,  where  he  assumed  supreme  power  as  perpetual 
dictate,  and  exterminated  the  party  of  Marius.  At  the 
end  of  the  war  all  the  Italians  obtained  Roman  citizen- 
ship, save  the  almost  annihilated  Samnites.  In  74  B.C. 
Mithridates  made  war  again,  and  having  been  defeated 
by  the  great  General  Pompey,  his  kingdom  was  sub- 
divided. Pompey  then  chastised  the  Pontic  king's 
allies,  erected  in  Syria  a  Roman  province,  and  took 
Jerusalem,  63  B.C.,  Palestine  then  remaining  under 
tributary  kings  as  before  mentioned. 

The  disorder  at  Rome,  and  the  conflicts  between  its 
leading  men,  had  become  extreme,  and  while  many 
desired  to  maintain  the  aristocratic  republic  which  had 
so  long  existed,  certain  clear-sighted  men  saw  that  it  was 
no  longer  in  a  condition  fit  to  rule  over  such  enormous 
and  varied  dominions. 

Amongst  those  who  strove  to  maintain  their  existing 
political  state  were  Pompey,  a  greatly  esteemed  citizen 
Cato,  and  the  world-renowed  orator  Cicero. 

Another  and  most  gifted  Roman  had  married  the 
daughter  of  Marius,  and  though  of  an  old  patrician 


346  ELEMENTS   OF   SCIENCE 

house,  espoused  the  popular  side.  He  did  this  the  more 
readily  because  his  many  gifts  enabled  him  to  control 
the  Roman  mob.  This  man  was  Julius  Ccesar,  who 
visited  Britain  and  conquered  the  whole  of  Gaul  from 
the  sea  to  the  Rhine. 

During  this  time  the  Roman  Government  became 
more  disordered  than  ever.  Then  Caesar  rebelled  (49 
B.C.)  and  marching  on  Rome  got  himself  chosen  Consul 
and  Dictator  by  the  people.  He  accumulated  offices, 
becoming  also  Pontifex  Maximus  or  High  Priest  of 
Rome,  and  assumed  the  title  of  Imperator  (Emperor  or 
Commander) — a  military  appellation  which  he  made 
exclusively  his  own.  After  defeating  Pompey  in  Epirus, 
and  his  other  enemies  in  Spain  and  Africa,  he  was,  as 
the  reader  knows,  killed  in  the  Senate  House  by  Cassius, 
Brutus,  and  others,  March  i5th,  44  B.C. 

Thereupon  followed  another  civil  war  between  Caesar's 
partisans,  under  his  great-nephew  and  adopted  son 
Octavius,  and  Mark  Antony — one  of  Caesar's  officers — on 
one  side,  and  the  supporters  of  the  republic  on  the 
other.  The  battle  of  Philippi  (42  B.C.)  in  Macedonia 
crushed  the  latter. 

Then  the  triumphant  Mark  Antony  fell,  through 
love,  to  be  the  creature  of  the  Egyptian  Queen 
Cleopatra,  and  these,  being  defeated  by  Octavius,  put 
themselves  to  death,  when  Egypt  became  another  Roman 
province.  Octavius,  who  had  been  adopted  by  Julius, 
was  also  Caesar,  and  a  new  title,  Augustus,  was  given  him 
by  the  people  of  Rome  (27  B.C.).  Thus  he  is  known  as 
the  Emperor  Augustus,  and  he  was  reigning  at  Rome 
when  Christ  was  born  in  Judaea.  Although  Augustus 
became  an  absolute  sovereign,  he  assumed  no  royal 
pomp,  appearing  but  as  a  citizen  who  was  the  first  and 
highest  magistrate,  while  the  old  republican  institutions 


HISTORY  347 

and  forms  continued  to  exist.  He  completed  the 
subjugation  of  Spain,  and  of  all  that  was  previously  un- 
conquered  south  of  the  Danube.  His  stepsons,  Tiberius 
and  Drusus,  with  the  son  of  the  latter  (Germanicus), 
also  endeavoured  to  subdue  the  Teutons  east  of 
the  Rhine,  penetrating  to  the  Elbe.  The  Romans  were, 
however,  driven  back  by  the  German  Arminius  (9  A.D.) 
and  never  obtained  any  permanent  hold  on  the  land  east 
of  the  Rhine  and  north  of  the  Mayn. 

The  great  distinction  of  the  Romans,  apart  from  their 
military  prowess  and  their  political  genius,  was  their 
instinct  for  legislation.  They  may  be  called  the 
originators  of  jurisprudence;  and  their  legal  system, 
which  began  to  be  elaborated  half  a  century  after 
Augustus,  has  had  an  enormous  influence  over  mediaeval 
and  modern  Europe,  and  its  influence  still  exists. 
Cicero  has  been  already  mentioned,  and  many  of  our 
readers  doubtless  are  acquainted  with  his  works.  Julius 
Caesar  was  also  hardly  less  celebrated  as  a  writer  than 
as  a  soldier.  The  memorable  poet  Lucretius  was  a 
contemporary  of  Cicero.  The  familiar  expression,  "  an 
Augustan  Age,"  however,  originated  from  the  fact  that 
the  time  of  the  second  Roman  Emperor  was  that  of  the 
most  celebrated  of  Roman  poets — Horace,  Virgil,  and 
Ovid,  as  also  of  the  historian  Livy. 

Augustus  reigned  forty-one  years,  and  was  succeeded 
by  his  adopted  stepson,  the  cruel  and  jealous  Tiberius 
(14  A.D.),  who  put  to  death  all  those  he  feared,  and  was 
succeeded  (37  A.D.)  by  Caligula  (grandson  of  Drusus) 
who,  after  four  years  of  mad  wickedness  of  all  kinds, 
was  killed  by  his  soldiers,  who  elected  his  uncle  Claudius 
in  his  place.  He  was  the  first  emperor  chosen  by  the 
army,  but  its  choice  obtained  the  ratification  of  the 
Senate.  Now  began  the  conquest  of  Britain,  which  was 


348  ELEMENTS   OF  SCIENCE 

visited  by  the  Emperor  (43  A.D.)  He  was  poisoned  by 
his  wife  and  niece,  Agrippina,  and  was  succeeded  (54 
A.D.)  by  Nero,  whom  Claudius  had  been  forced  by  his  wife 
to  adopt.  After  beginning  well,  he  became  one  of  the 
most  horribly  corrupt  of  all  emperors,  even  causing  his 
own  mother  to  be  slaughtered.  Having  been  deposed 
by  the  Senate  after  a  reign  of  fourteen  years,  he  died  by 
his  own  hand  68  A.D. 

Thereupon  ensued  a  period  of  conflict  and  confusion, 
emperors  being  chosen  by  the  military  in  different 
regions,  some  of  them  for  a  time  obtaining  possession  of 
Rome  and  legal  recognition,  as  did  Galba,  Otho,  and 
Vitellius.  It  was  during  and  after  this  period  that  the 
poet  and  satirist  Lucian  lived. 

A  more  settled  state  of  things  was  initiated  (70  A.D.) 
by  the  choice  of  Vespasian,  by  whom,  in  conjunction 
with  his  son  Titus,  Jerusalem  was  destroyed.  The  latter 
succeeded  his  father,  79  A.D.  but  died  aftei-  a  reign  of 
but  two  years,  universally  regretted,  to  be  succeeded  by 
his  brother  Domitian,  a  most  horrible  tyrant,  but  who 
was  not  killed  till  96  A.D.  In  his  reign  the  Roman 
general  Agricola  completed  the  conquest  of  England, 
and  war  began  with  the  Dacians — a  people  who  in- 
habited what  is  now  Hungary  east  of  the  Theiss,  with 
Rouinania  and  Bessarabia,  and  an  adjacent  slip  of  what  is 
now  Russia.  It  was  in  the  year  of  the  accession  of 
Titus  that  the  celebrated  man  of  science,  Pliny,  met  his 
death  by  incautiously  approaching  too  near  to  Vesuvius 
at  the  time  of  that  eruption  which  destroyed  Pompeii, 
Another  most  celebrated  historian  of  this  period,  to 
whom  we  owe  a  description  of  the  Germans,  was 
Tacitus. 

After  the  two  years  reign  of  the  Emperor  Nerva, 
Trajan  became  emperor  (98  A.D.),  and  reigned  till  117, 


HISTORY 


349 


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350  ELEMENTS   OF  SCIENCE 

He  was  a  Spaniard,  and  only  twenty-five  years  old  when 
he  came  into  power.  In  his  reign  the  Roman  Empire 
attained  its  greatest  extent.  Through  conquests  over 
the  Parthians,  it  reached  from  the  Caspian  to  the 
Persian  Gulf,  while  Dacia  was  also  subdued  and  annexed. 
Thus  the  empire  never  included  either  Bohemia  or 
Moravia,  or  Austro-Hungary  between  the  Danube  and 
the  Theiss,  nor  any  part  north  of  the  Danube  between 
Pesth  and  Donauwerthe. 

With  this  emperor  we  enter  upon  the  eventful  second 
century  of  the  Christian  era.  His  successor,  Hadrian, 
was  a  Roman  by  birth,  who  reigned  from  117  to  138. 
He  had  accompanied  his  predecessor  in  most  of  his 
expeditions  and  subsequently  visited  almost  all  the 
provinces  of  the  empire.  In  England  he  built  the  well- 
known  wall  to  keep  off  the  northern  tribes.  He  had 
hardly  succeeded  to  power  when  the  boundaries  of  the 
empire  began  to  recede,  and  he  at  once  made  peace  with 
the  Parthians,  and  yielded  up  great  part  of  his  prede- 
cessor's conquests  over  them. 

The  next  two  emperors  were  the  most  celebrated  of 
all  for  their  morality  and  piety.  The  first  of  these,  who 
had  been  adopted  by  Hadrian,  was  Antoninus  Pius  and 
was  the  son  of  a  Roman  consul.  He  came  into  power 
138  A.D.,  and  reigned  twenty-three  years,  leading  a  life 
of  most  exemplary  benevolence  and  temperance.  His 
only  war  was  in  England,  wherein  he  extended  the 
Roman  dominion,  building  a  second  wall  to  keep  out  the 
unsubdued  inhabitants  of  Scotland.  He  adopted  his 
successor,  Marcus  Aurelius,  who  espoused  his  unworthy 
daughter  Faustina.  He  succeeded  to  power  161  A.D., 
and  reigned  nineteen  years  with  the  esteem  and  admira- 
tion of  his  subjects.  But  many  troubles  took  place 
during  his  supremacy,  and  he  had  to  exert  the  greatest 


HISTORY  351 

efforts  to  preserve  the  empire  from  further  diminution. 
On  his  death,  180  A.D.,  a  son  for  the  first  time  succeeded 
his  father.  This  was  Commodus,  who  was  a  monster  of 
vice  and  cruelty,  and  was  murdered  after  a  reign  of 
twelve  years.  A  worthy  successor,  Pertinax,  was  chosen, 
but  was  murdered  in  less  than  three  months  by  the 
soldiery,  who  then  sold  the  empire  to  Didius  Julianus, 
who  was  beheaded  after  sixty-six  days,  when  Septimus 
Severus,  an  African,  having  avenged  Pertinax,  reigned 
from  193  to  211.  Thus  his  reign  introduces  us  into  the 
third  century  of  our  epoch.  He  was  succeeded  by  both 
his  sons,  Geta  and  Caracalla,  with  such  hatred  and 
jealousy  between  them  as  a  consequence,  that  the  former 
was  soon  murdered.  His  successful  rival,  a  monster  who 
by  his  cruelty  afflicted  the  whole  empire,  was  in  turn 
murdered  217  A.D. 

After  a  brief  attempt  to  hold  power  by  the  militarily 
elected  Macrinus,  he  was  succeeded  by  two  Syrian  youths, 
each  a  son  of  two  sisters,  daughters  of  Caracalla.  The 
first,  Reliogabalus,  was  a  priest  of  the  Sun,  and  in  him  Rome 
for  the  first  time  became  subject  to  an  Eastern  sovereign. 
He  was  a  wonderful  example  of  effeminacy  and  vice,  who, 
having  been  murdered  by  his  guards  222  A.D.,  was 
succeeded  by  his  worthy  cousin,  Alexander  /Severus,  under 
whom  the  empire  enjoyed  unwonted  happiness.  He,  in 
turn,  was  murdered  A.D.  235,  owing  to  a  conspiracy  of 
his  successor  Maximin,  who,  though  born  within  the 
empire,  was  by  blood  a  Goth. 

From  the  time  of  the  Antonines  (Pius  and  Marcus 
Aurelius)  the  condition  of  the  inhabitants  of  the  Roman 
provinces  was  greatly  ameliorated,  and  by  the  beginning 
of  the  third  century  all  the  inhabitants  of  the  provinces, 
who  were  not  slaves,  had  become  Roman  citizens.  Thus 
the  empire  had  become  a  monarchy — a  homogeneous 


352  ELEMENTS   OF   SCIENCE 

mass  of  people  ruled  by  a  chief  who  was  more  than  a 
king,  save  for  that  title  and  the  absence  of  a  settled 
hereditary  succession.  As  the  city  of  Rome  had  thus 
gradually  waned  and  lost  all  real  sovereignty,  so  the 
power  of  the  emperors  had  waxed  and  become  estab- 
lished. 

Alexander  Severus  was  compelled  to  wage  war  with 
the  Persians,  who  (in  the  year  226)  revolted,  and  under 
their  first  king,  Artaxerxes,  occupied  the  territory  of  the 
Parthian  kingdom. 

Maximin,  by  his  tyranny  having  excited  universal 
hatred,  was  declared  a  public  enemy  by  the  Senate,  which 
named  two  illustrious  Romans,  the  Gordians  (father  and 
son),  as  emperors — only  to  lose  their  lives  in  little  more 
than  a  month.  Then  Maximus  and  Balbinus  were  de- 
clared joint  emperors,  and  Maximus,  in  the  ensuing  con- 
test, was  murdered  with  his  son  at  Aquileia  (238  A.D.), 
as  were  also  his  successful  opponents  in  the  same  year. 
A  third  Gordian  was  then  made  emperor,  but  was  assas- 
sinated and  succeeded  by  Philip,  an  Arab  raised  to 
power  by  the  soldiery,  in  the  year  244.  He  celebrated 
with  magnificence  public  games,  and  also  the  thousandth 
year  of  Rome's  existence.  He  was  defeated  in  a  struggle 
with  Decius  who  had  been  a  senator,  and  became 
emperor  249  A.D. 

Then  the  Goths  (a  people  who,  migrating  from  further 
north,  occupied  Dacia  and  crossing  the  Danube  invaded 
the  empire)  descended  into  Illyria ;  when  Decius,  after 
successfully  combating  them,  was  drowned,  251  A.D. 
His  successor,  Gallus,  was  slain  after  a  military  revolt 
(in  the  year  253),  and  was  succeeded  by  Valerian,  who,  in 
about  his  sixtieth  year,  was  elected  by  the  unanimous 
voice  of  the  Roman  world.  He  was  a  man  of  noble  birth, 
learned,  and  of  mild  and  unblemished  manners,  but  who 


HISTORY  353 

associated  with  his  power  his  youthful  but  corrupt  son 
Gallienus.     Then  the  empire  was  attacked  on  all  sides 
by  the  Teutonic  tribes  known  as  Franks  and  Alemanni, 
by  the  Goths  and  by  the  Persians.    The  Franks  invaded 
Gaul   and   thence   passed  to  Spain   and   onwards   into 
Africa,  while  the  Alemanni,  crossing  the   Alps,  pene- 
trated  almost   to   Rome   itself,    only,   however,    to   be 
repulsed.     The   Goths,  after   dominating  what   is  now 
Constantinople  and  part  of  Asia  Minor,  passed  on  (253 
A.D.),  ravaging  Greece,  plundering  the  Temple  of  Delphi, 
and  threatening   Italy.     But   Valerian   felt   bound   to 
try  and  punish  the  hostility  of  the  Persian  king  Sapor ? 
and  so  crossed  the  Euphrates.      He  was  defeated  and 
taken  prisoner  (260  A.D.),  and  died  in  captivity.      The 
power  of  Persia  long  endured,  and  was  governed  by  the 
descendants  of  Artaxerxes   (called  the  Sassanidce)   for 
four  hundred  years.     Under  the  remaining  sovereign, 
Gallienus,  the   whole   empire  became  divided  between 
various  pretenders  to  the  imperial  power,  who  all  met 
with  violent  deaths,  while  the  universal  confusion  and 
disorder  greatly  diminished  the  population  of  the  empire. 
In  the  year  268  Gallienus  died  and  was  succeeded  by 
Claudius,  who   after   gloriously   routing  the  Goths  at 
Nissa  (in  what  is  now  Servia),  died  (270  A.D.),  and  was 
succeeded  by  Aurelian  who,  like  Claudius,  was  an  Illyrian. 
In  a  reign  of  but  four  years  he  recovered  Gaul,  with 
Britain  and  Spain,  but  had  to  relinquish  Dacia  to  the 
Goths.     Assassinated  in  the  year  275,  he  was  succeeded 
by  Tacitus,  who  in  little  more  than  six  months  was  again 
succeeded  by  an  Illyrian  named  Probus.     He  in  turn 
was  killed  by  his  soldiers  in  282,  after  delivering  Gaul, 
invading  Germany,  building  a  wall  from  the  Rhine  to 
the  Danube,  and  recruiting  the  Roman  army  from. the 
German  tribes,    -Next  came  Cm*us>  who  delivered  Illyria 

z 


354  ELEMENTS   OF  SCIENCE 

from  the  Barbarians,  and  having  victoriously  invaded 
Persia  beyond  the  Tigris,  died  mysteriously  in  December 
284.  His  two  sons,  Carinus  and  Numerian,  succeeded 
him,  whereof  the  latter  died  the  following  year.  His 
unworthy  brother  alienated  by  his  vices  the  hearts  of 
the  people,  and  Diocletian,  commander  of  the  Imperial 
Body  Guard,  was  chosen  emperor.  Diocletian  advanced 
to  meet  Carinus  in  Moesia,  when  the  troops  of  the  latter 
were  entirely  victorious,  but  in  the  moment  of  success  he 
was  stabbed  in  revenge  for  a  private  wrong  (A.D.  285). 

With  the  successful  Emperor  Diocletian  began  a  new 
epoch  of  the  Roman  Empire,  though  he  was  but  the  son 
of  parents  who  had  been  slaves,  while  his  mother  was  a 
native  of  Dalmatia,  which  ultimately  became  his  chosen 
residence.  The  changes  he  effected  were  greatly  facili- 
tated by  the  length  of  his  reign,  which  lasted  twenty 
years.  He  introduced  an  Oriental  magnificence  of 
royalty,  assuming  a  diadem  and  introducing  Persian 
ceremonial.  His  despotism  was  more  concentrated  than 
ever,  though  administered  through  an  enormous  bureau- 
cracy. All  provincials  being  formally  acknowledged 
Roman  citizens,  the  city  of  Rome  lost  still  more  in  im- 
portance, while  the  royal  residence  was  usually  either  in 
Milan  or  Nicomedia.  Diocletian  made  important  changes 
in  the  constitution  of  the  empire,  as  to  which  the  student 
is  referred  to  histories  of  Rome.  He  abdicated  the 
imperial  dignity  303  A.D.,  and  retired  to  Dalmatia, 
where  he  expired,  having  erected  a  magnificent  palace 
the  ruins  of  which  still  exist  at  Spalatro. 

He  had  associated  with  him  in  power  Maximian,  Con- 
stantius,  and  Galerius,  and,  after  his  abdication,  great 
disorder  ensued.  Constantius  governed  the  province  of 
Gaul  and  was  favourable  to  Christianity.  He  died  306 
A.D.,  and  his  son  Constantine  took  his  place.  Maximian, 


HISTORY  355 

who  had  abdicated  with  Diocletian,  was  replaced  by  his 
son  Maxentius,  who  in  the  year  306  was  declared 
emperor  at  Rome.  Thereafter  great  confusion  and 
dissension  arose,  there  being  six  claimants  for  the 
empire,  and  Maximian  re-entered  the  political  arena. 
In  312  A.D.  civil  war  broke  out  between  Constantine 
and  Maxentius.  When  near  Rome,  the  former  defeated 
his  opponent,  who  was  drowned  and  afterwards  decapi- 
tated. Eleven  years  later,  he  defeated  the  last  of  his 
opponents.  In  the  year  324  Constantine  became  sole 
sovereign  of  the  entirely  re-united  empire.  With  Con- 
stantine two  notable  events  took  place :  the  first  of 
these  was  that  the  seat  of  the  empire  was  transferred 
from  Rome  to  the  newly  built  Byzantium,  now  Constan- 
tinople. The  second  event,  which  was  of  inexpressibly 
more  importance,  was  that  for  the  first  time,  in  the 
person  of  Constantine,  Christianity  mounted  the  im- 
perial throne,  which  thenceforth,  save  for  the  brief  reign 
of  Constantine's  nephew,  the  Emperor  Julian — from 
361  to  363  A.D. — continued  officially  Christian  till 
the  extinction  of  the  last  shadow  representing  it  was 
abolished,  1806  A.D. 

Such  being  a  brief  sketch  of  landmarks  in  the  civil 
and  political  history  of  Rome,  it  but  remains  to  con- 
sider briefly  the  religion  and  philosophy  of  the  Roman 
people.  A  knowledge  of  these,  together  with  Roman 
political  history  down  to  Constantine,  may  enable  the 
student  to  understand  how  the  Roman  civilisation, 
acting  on  races  settled  within  the  empire,  has  produced 
that  European  world  which  now  exists. 

The  religion  of  the  Romans  was  very  different 
from  that  of  Greece.  Their  gods — mostly  survivals  of 
the  deities  of  the  tribes  whose  union  founded  Rome — 
had  hardly  any  legendary  histories  such  as  those  which 


356  ELEMENTS   OF   SCIENCE 

pertained  to  the  divinities  of  Olympus,  while  they  were 
served  with  greater  devotion  and  more  respect.  Strong, 
however,  as  was  the  religious  sentiment  of  the  Romans, 
and  important  as  everything  was  deemed  which  related 
to  the  worship  of  the  gods,  nevertheless  this  induced  no 
tendency  towards  a  theocracy.  Religion  was  entirely 
subordinated  to  the  State,  and  its  priests  had  also  civil 
functions,  not  as  priests  but  as  citizens :  they  were 
thorough  laymen,  and  not  animated  by  the  sacerdotal 
spirit.  Religion  consisted  of  formal  acts,  and  not  in  the 
acceptance  of  dogmas  or  in  devout  aspirations.  The  pious 
man  was  he  who  knew  well  how  to  honour  the  gods 
according  to  the  laws  of  the  State,  and  who  presented 
himself  in  the  temples  properly  dressed,  in  prescribed 
attitudes — the  priest  serving  but  as  a  master  of  the 
ceremonies,  and  to  read  the  formulae  which  the 
worshipper  had  to  repeat. 

It  was  a  religion  which  accustomed  the  people  to 
discipline  and  obedience,  and  was  essentially  much 
more  moral  than  that  of  Greece.  The  Romans  believed 
that  it  was  through  religion — the  aid  of  the  gods, 
especially  Jupiter — that  they  had  conquered  the  world, 
and  Rome  was  considered  by  the  Greeks,  as  well  as  by 
its  own  inhabitants,  to  be  the  most  religious  city  in  the 
world. 

At  an  early  period,  however,  many  of  the  Greek  and 
Roman  gods  became  fused  and  confounded  together  • 
and  other  pagan  religious  influences  from  the  East  came 
afterwards  to  exercise  a  powerful  influence  on  the  beliefs 
and  practices  of  the  Italians. 

Towards  the  close  of  the  republic,  a  profound  spirit 
of  scepticism  had,  indeed,  asserted  itself  in  Rome ;  and 
Cicero  and  Csesar  (and  the  writings  of  Lucretius)  may  be 
taken  as  examples  of  the  unbelieving  spirit  of  Roman 


HISTORY  357 

society  in  their  day — though  they  upheld  the  external 
practices  which  were  traditions  of  the  State. 

With  the  advent  of  Augustus,  a  renovation  of  Roman 
religion  commenced.  He  sought  its  political  support, 
rebuilt  temples  which  had  fallen  into  decay,  introduced 
fresh  objects  of  worship,  and  sought  to  institute  moral 
reforms.  He  associated  himself  with  the  various  priest- 
hoods, and  became  Pontifex  Maximus  himself. 

A  practice  arose  of  deifying  deceased  emperors,  which, 
strange  as  it  may  seem  to  us,  was  but  the  continuation, 
or  revival,  of  a  practice  of  very  ancient  date  in  Egypt 
and  elsewhere.*  Ultimately  the  worship  of  a  recently 
deceased  emperor  came  to  be  a  most  conspicuous  one  in 
the  Roman  provinces,  especially  as  a  manifestation  of 
loyalty  to  the  State. 

In  the  Augustan  Age  it  became  the  fashion  to  admire 
the  simplicity  and  piety  of  earlier  days,  and  Horace,  and 
above  all,  Virgil,  were  incited  by  the  emperor  to  promote 
this  sentiment.  That  well-known  poem,  the  JZneid,  of 
the  last-named  poet,  was  essentially  a  religious  one,  and 
has  had  great  influence  on  religion  down  to  our  day. 

The  terrible  times  of  Tiberius  and  Caligula  were  not 
likely  to  weaken  the  influence  of  religion,  nor  did  the 
spirit  of  scepticism  again  raise  its  head  at  any  period  of 
the  empire  as  it  had  under  the  republic. 

As  the  Roman  religion  was  devoid  of  dogma,  so  also 
was  it  devoid  of  any  spirit  of  either  proselytism  or  in- 
tolerance. Indeed  the  Romans  for  a  time  viewed  with 
jealousy  any  worship  by  strangers  of  their  Jupiter  of  the 
Capitol,  from  the  same  spirit  which  made  them  seek  to 
wrest  from  their  opponents  the  succour  of  their  various 
gods,  by  themselves  showing  great  respect  and  reverence 

*  See  ante,  p.  323. 


358  ELEMENTS   OF   SCIENCE 

to  them.  But  although  for  a  time  the  worship  of 
foreign  deities  in  Rome  was  forbidden,  later  on  there 
was,  as  it  were,  an  interchange  of  religious  worship  all 
over  the  Empire,  and  thus  a  sort  of  universal  pagan 
church — a  church  of  practices,  not  doctrines — preceded 
the  diffusion  of  a  universal  Christian  church. 

So  it  came  about  that  Isis  and  Serapis  were  wor- 
shipped at  Rome  in  the  second  century  after  Christ. 

The  Oriental  religions  differed  generally  from  that  of 
Rome  in  their  more  sacerdotal  and  emotional  character. 
Worshippers  were  invited  to  mourn  over  the  death  of  an 
Adonis,  to  sympathise  with  a  divine  mother  wrho  sees  the 
beauteous  Athis  expire  in  her  arms,  or  to  rejoice  at  the 
resurrection  of  a  god  such  as  Osiris.  These  practices, 
mixed  with  sanguinary  rites  and  devotions  of  very 
doubtful  morality,  began  to  exercise  great  influence  over 
the  lower  classes  of  Italy,  and  above  all  of  Rome.  But 
such  beliefs  and  worships  readily  accommodated  them- 
selves to,  and  harmonised  with,  the  State  religion,  as 
also  did  the  widely  diffused  and  very  successful  Oriental 
worship  of  Mithra. 

During  the  period  which  elapsed  between  the  days  of 
the  republic  and  the  end  of  the  second  century,  a  tendency 
arose  to  recognise  one  God  as  supreme  over  all  other 
gods,  or  even  to  revere  one  solely  existing  God ;  and 
this  tendency  grew  and  developed  itself.  Nevertheless 
the  educated  Romans  of  the  period  of  Cicero,  and  for  a 
time  afterwards,  were  doubtful  with  respect  to  a  future 
life.  Under  the  empire,  however,  scepticism  in  this 
respect  tended  to  diminish,  while  the  great  influence  of 
that  belief  and  the  vivid  fears  it  inspired,  are  attested  by 
the  number  of  associations  formed  (in  which  even  slaves 
bore  their  part)  for  the  purpose  of  providing  their 
members  with  the  requisite  funeral  rites  and  sepulture. 


HISTORY  359 

Jealous  as  was  the  State  generally  of  all  private  associa- 
tions, they  were  freely  permitted  for  this  one  purpose, 
and  for  the  feasts  and  sacrifices  therewith  connected. 

After  these  few  words  we  must  turn  from  the  con- 
sideration of  Roman  religion  to  that  of  philosophy  at 
Rome.  Roman  philosophy,  and  Roman  art  also,  were 
not  products  of  the  soil,  but  imported  from  Greece,  which 
became,  under  the  empire,  the  acknowledged  model  and 
leader  in  the  arts  and  amenities  of  life.  Despised  in  the 
earlier  days  of  the  republic,  Hellenism  became  later  a 
universal  fashion.  Thus,  when  Carneades*  came  to 
Italy,  he  was  soon  sent  back  to  Greece  by  Cato  the 
censor  (the  great-grandfather  of  the  Cato  before  men- 
tioned t),  and  philosophy  did  not  become  established  in 
Roman  society  till  the  time  of  Cicero. 

It  was-  the  school  of  Epicurus  *  and  the  rival  school 
of  the  Stoics,|  which  successively  prevailed  at  Rome, 
the  former  mainly  in  the  later  republic  and  the  early 
days  of  the  empire,  but  the  latter  afterwards.  Stoicism 
may  be  said  to  have  been  the  main  and  dominant 
philosophy,  and  it  accorded  well  with  all  that  was 
noblest  and  best  in  the  tendencies  of  the  Roman  people. 
It  was  a  philosophy  which  inculcated  and  promoted 
all  charitable  and  benevolent  movements;  the  kinder 
treatment  of  slaves,  whose  very  lives  were,  at  first,  by 
law,  entirely  at  the  mercy  of  their  masters,  and  who 
formed  so  very  large  a  part  of  the  entire  population. 

The  most  illustrious  of  the  Roman  Stoics  was  Seneca, 
who  began  to  write  under  Caligula,  was  exiled  by  Claudius, 
then  recalled  and  made  a  tutor  of  Nero,  who  ultimately 
sentenced  him  to  death  on  a  charge  of  treason.  The 


*  See  ante,  p.  330.  t  See  ante,  p.  345. 

t  See  ante,  loc.  cit. 


360  ELEMENTS   OF   SCIENCE 

teaching  of  Seneca  was  of  such  a  refined  and  elevated 
morality,  that  it  has  been  mistakenly  attributed  to 
Christian  influence.  That  Stoicism  penetrated  and 
prevailed  throughout  Roman  society  is  shown  by  the 
fact  that  one  of  its  most  celebrated  teachers  was  the 
slave  Epictetus,  while  it  ascended  the  throne  with  the 
Antonines,  being  encouraged  by  Antoninus  Pius  and 
actually  professed  and  taught  by  Marcus  Aurelius. 

By  the  end  of  the  second  century  many  sorts  of 
philanthropic  and  charitable  efforts  had  been  instituted 
in  Rome,  and  such  tendencies  increased,  at  the  same 
time  with  devoutness  in  religion,  solicitude  about  a 
future  life,  the  sacerdotal  spirit,  and  a  tendency  towards 
monotheism. 

But  a  new  departure  in  philosophy  became  developed 
in  Egypt  from  the  combined  influences  of  Hellenic 
culture  and  Jewish  religion.  This  was  the  school  of  the 
Neo-Platonists  of  Alexandria  which,  beginning  in  the  days 
of  Augustus,  greatly  influenced  the  Roman  world.  Its 
effects  indeed  are  widely  diffused  even  at  the  present  day. 
Alexandria  had  developed  enormous  commercial  industry 
and,  with  its  consequent  wealth,  had  become  a  meeting- 
place  for  various  races  and  civilisations,  and  a  great 
intellectual  centre,  under  dominant  Hellenic  influence. 
The  first  renowned  member  of  the  new  Alexandrian 
school  was  the  Hellenic  Jew  Philo,  who  was  born  about 
25  B.C.  His  philosophy  was  essentially  theological.  He 
taught  that  the  only  true  existence,  in  the  highest  sense, 
is  God,  dwelling  apart  and  acting  on  the  world  through 
an  intermediate  being,  the  "  Word  "  (in  Greek  Logos), 
dwelling  with  God  as  his  wisdom  (in  Greek  Sophia), 
and  emanating  into  numerous  subordinate  spiritual 
agencies.  The  "Word"  was  not  eternal  but  generated 
by  God  in  a  peculiar  manner,  and  it  was  this  His  "  first 


HISTORY  361 

begotten  "  who  had  created  the  world.  As  to  what  it 
was  desirable  to  do,  Philo  taught  that  logic  and  reason- 
ing are  of  relatively  little  value,  and  that  the  highest 
philosophy  consisted  in  the  acquirement  of  a  direct 
intuition*  of  God,  to  be  attained  as  a  reward  for  com- 
plete self-renunciation  and  resignation  to  divine  influence. 

Thus  the  Neo-Platonic  school  was  essentially  mystical, 
and  renounced  all  appeals  to  reason  as  the  one  only 
source  of  the  highest  knowledge.  Philo  visited  .Rome  in 
40  A.D.,  and  doubtless  there  exercised  a  direct  influence. 
But  the  school  of  Alexandria  accompanied  the  rise,  and 
combated  the  spread,  of  Christianity. 

The  religion  destined  to  play  so  great  a  part  in  trans- 
forming the  world  naturally  appeared  at  first  to  the 
Greeks  and  Romans  as  an  obscure  sect  of  the  Jews. 
The  latter  were  early  regarded  as  an  impious  race  which 
despised  the  gods,  and  would  not  ever  worship  the 
emperors,  for  which  refusal  they  suffered  cruel  persecu- 
tions. The  inhabitants  of  Antioch  burnt  alive  many  who 
would  not  abjure  their  creed,  and  fifty  thousand  Jews 
are  said  to  have  been  massacred  at  Alexandria. 

The  Pagans  could  not  understand  the  obstinacy  of 
Jews  and  Christians  in  refusing  to  worship  Roman  gods, 
whose  clients  were  so  willing  to  venerate  what  was 
adored  by  either  Christians  or  Jews.  Romans  were 
willing  to  recognise  in  Jehovah  their  own  Jupiter,  and 
Alexander  Severus  t  erected  an  image  ©f  Christ  amongst 
the  deities  of  his  private  chapel.  But  the  refusal  of 
Christians  to  worship  the  gods  in  any  way,  and  their 
repeated  declarations  that  the  gods  of  the  empire  were 
but  idols  to  be  execrated,  drew  on  them  the  persecutions 
and  sufferings  they  had  to  endure,  not  only  under 


*  As  to  this  word,  see  ante,  p.  261.  t  See  ante,  p.  351. 


362  ELEMENTS    OF   SCIENCE 

monsters  like  Nero,  but  under  such  virtuous  sovereigns 
as  Antoninus  Pius  and  Marcus  Aurelius.  In  202  A.D., 
Severus  instituted  a  persecution  which  lasted  about  ten 
years.  A  short  but  very  severe  and  universal  persecution 
also  took  place  under  Decius,*  which  was  renewed  by 
Valerian,  257  A.D.  In  303,  Diocletian  ordered  all  the 
sacred  buildings  and  books  of  the  Christians  to  be 
destroyed,  and  his  persecution  was  one  of  the  most 
severe  of  all ;  but  it  was  the  last. 

The  exceedingly  rapid  spread  of  Christianity  through 
the  empire  is  largely  to  be  accounted  for  by  the  pre- 
paration unconsciously  made  for  it  in  pious  minds  by 
that  fermentation  of  religion  and  philosophy  at  Home, 
which  took  place  during  the  first  two  centuries  of  our 
era,  as  has  above  been  briefly  indicated.  The  changes 
which  thus  prepared  the  way  for  Christianity  were  :  (i) 
the  revival  of  Roman  religion  under  Augustus  ;  (2)  its 
progress  up  to  and  beyond  the  time  of  the  Antonines ; 

(3)  the    inculcation  of   benevolence  and  philanthropy  ; 

(4)  the  anxiety  as  to  the  state  of  the  soul  after  death, 
and  the  fears  of  such  infernal    punishments    as  were 
depicted  by  Virgil ;  (5)  the  increasing  tendency  towards 
monotheism  ;  and   (6)  the  sacerdotalism  introduced  with 
the  advent  of  Pagan  religions  from  the  East. 

To  the  wants  thus  indicated,  Christianity  marvellously 
responded,  and  the  good  tendencies  previously  developed 
were  by  it  greatly  intensified.  The  old  system,  without 
Christianity,  could  never  have  adequately  responded  to 
the  needs  and  aspirations  of  the  men  of  those  days,  and 
for  the  following  reasons:  (i)  however  strong  or  wide- 
spread might  have  been  the  tendency  amongst  the  Pagans 
to  attain  to  a  conception  of  the  unity  of  God,  it  was 
impossible  for  them,  while  maintaining  their  polytheistic 

*  See  ante,  p.  352. 


HISTORY  363 

worship,  to  arrive  at  a  distinct,  well-defined,  and  general 
consent  concerning  it ;  (2)  the  moral  advance  made 
under  Paganism  was  considerable,  but  eo  long  as  the 
legends  of  the  gods  were  tolerated,  and  certain  of  their 
rites  practised,  any  approach  to  a  perfect  system  of 
morality  was  unattainable ;  (3)  popular  devotion,  however 
stimulated  by  introduction  from  the  East,  remained 
essentially  material  and  devoid  of  exalted  aspirations ; 
(4)  philosophy,  though  appealing  to  the  cultured  few, 
made  no  sufficient  efforts  to  attain  the  popular  ear  and 
reach  the  masses  ;  (5)  it  was  impossible  to  avoid  a  pro- 
found distinction  between  the  ideas  and  convictions  which 
actuated  the  well-disposed  men  of  education,  and  those 
which  acted  upon  the  bulk  of  the  population-;  (6) 
need  was  felt  for  a  religion  consisting  not  of  external 
forms,  but  of  distinct  and  definite  dogmas,  funda- 
mentally identical  in  their  claim  upon  the  assent  and 
obedience  of  rich  and  poor,  and  accompanied  by  distinct 
unequivocal  precepts.  The  Christian  religion,  so  un- 
compromising and  distinct  in  its  commands  and  dogmas, 
coupled  a  lofty  morality  with  the  foundation  of  its  faith ; 
its  enunciation  of  the  unity  of  God  was  plain  and 
unequivocal,  and  its  theology  was  free  from  all  admixture 
with  gross  and  criminal  fables.  It  appealed  both  to  the 
cultured  and  the  uneducated,  and  it  commanded  obedience 
of  the  will,  while  it  incited  the  emotions  to  aspire  after  the 
loftiest  conceivable  ideals.  Its  spread  was  greatly  aided 
by  that  freedom  accorded  to  associations  for  performing 
funeral  rites,  before  noticed.  In  this  character  Chris- 
tians were  easily  able  to  assemble  for  worship  and 
mutual  edification,  and  we  may  see  abundant  evidnces 
of  this  in  the  Catacombs  of  Rome  to-day.  Christianity 
had  already  spread  far  and  wide  in  the  time  of  Decius. 
It  became  socially  predominant  under  Constantine  by 
whose  authority  the  well-known  Council  of  Nice  was 


364  ELEMENTS   OF   SCIENCE 

convoked,  Under  his  son  Constantius,  Paganism  began 
to  be  persecuted,  and  Julian  (the  son  of  a  brother  of 
Constantine),  in  his  fruitless  attempt  to  revive  Paganism, 
was  rather  seeking  to  oppose  to  Christianity  a  new 
Hellenic  religion  of  his  own  devising,  than  trying  really 
to  restore  the  old  worship  of  Rome  and  Italy.  The 
school  of  Alexandria,  though  it  opposed,  really  helped 
to  promote  and  develop,  the  theology  of  the  Christian 
Church;  and  ultimately,  in  the  time  of  the  Emperor 
Theodosius  (367  to  375  A.D.),  all  public  profession  of  the 
religion  of  Pagan  Rome  finally  ceased. 

With  this  brief  and  elementary  sketch  of  the  history 
of  the  rise  and  development  of  the  Christian  empire 
we  must  here  content  ourselves,  referring  the  student  to 
the  various  historical  works  wherein  he  will  find  depicted 
the  struggles  which  eventuated  in  (i)  the  destruction 
of  the  western  half  of  the  empire;  (2)  the  establishment 
of  the  existing  European  nations;  (3)  the  rise  and 
gradual  extension  of  the  recognised  prominence  and 
and  power  of  the  Bishop  of  Rome  (which  followed  so 
naturally  the  traditions  of  the  city  of  Rome,  as  having 
possessed  in  an  eminent  degree  the  genius  of  legislation, 
orderly  rule,  and  universal  dominion) ;  (4)  the  tempo- 
rary eclipse  of  antecedent  culture  and  civilisation;  (5) 
the  gradual  awakening  of  the  spirit  of  inquiry ;  (6)  the 
discovery  of  the  previously  unknown  half  of  the  globe ; 
(7)  the  schools  of  philosophy  which  from  time  to  time 
arose  up  to  our  own  day  ;  (8)  the  rapid  advance  of 
physical  science ;  and  (9)  the  rise  of  the  conception  of 
human  progress.  These  can  be  but  mentioned  here, 
our  intention  being  to  present  our  readers  with  no  more 
than  an  introduction  to  such  elementary  historical 
knowledge  as  may  serve  to  incite  them  to  pursue  the 
great  science  of  human  history. 


CHAPTER  X 
SCIENCE 

THE  beginner  who  has  attentively  read  the  preceding 
chapters  of  this  little  work  will  have  been  introduced  to 
the  elements  of  the  physical  sciences  and  also  to  those  of 
psychology  *  and  of  logic. 

We  saw  at  the  outset  t  that  there  is  one  property 
common  to  all  those  things  we  have  successively  passed 
in  review — namely,  the  property  of  number.  But  there 
is  another  quality  which  is  also  common  to  every  well- 
founded  perception  we  have  gained,  whatever  has  been 
the  nature  of  the  objects  considered.  That  quality,  or 
property,  is  truth.  J 

It  is  a  matter  of  course  that  no  scientific  conclusion, 
or  doctrine,  can  be  worth  anything  if  it  is  not  "  true," 
as  also  that  every  scientific  inquiry  is  necessarily  an 
inquiry  after  "  truth " — after  truths  of  one  kind  or 
another. 

Now  the  tests  of  truth  are  different  in  different  lines 
of  investigation.  In  mechanics  and  the  study  of  physical 
forces  we  may  often  avail  ourselves  largely  of  experi- 
ment, as  also  in  the  study  of  the  living  world.  In 
Palceontology,  §  however,  we  can  but  make  use  of 


See  ante,  pp.  252  and  268.  t  See  ante,  p.  5. 

See  ante,  p.  260.  §  See  ante,  p.  244. 


366  ELEMENTS   OF   SCIENCE 

observation   and    of   inference,    and   inference   plays   a 
yet  larger  part  in  many  historical  investigations. 

But  we  may  occupy  ourselves  not  with  what  may  be 
the  truth  in  this  or  that  scientific  inquiry,  but  about  the 
different  kinds  of  truth  attainable  in  different  inquiries. 
The  sort  of  truth  to  be  gained  by  the  study  of  the 
geometry  of  Euclid  is  evidently  different  in  nature 
from  that  afforded  by  investigations  as  to  animal  physio- 
logy.* This  leads  us  to  the  question  of  the  different 
degrees  of  truth  which  different  inquiries  may  be  able  to 
afford  us,  and  so  we  may  pass  on  from  considering  what 
are  the  tests  to  be  applied,  and  their  value,  in  different 
branches  of  knowledge,  to  the  question  whether  there  is 
any  one  test  we  can  apply  to  the  ultimate  and  funda- 
mental propositions  of  every  branch  of  knowledge ;  and 
if  so,  what  that  one  test  may  be  ? 

Thus  the  various  sciences  have  each  their  own  funda- 
mental truths  which  are  vouched  for  and  shown  to  be 
valid  by  their  own  proper  tests.  But  we  should  endeavour 
to  see  whether  there  are  any  truths  which  underlie  all 
sciences,  and  if  so  what  they  are,  and  what,  if  anything, 
vouches  for  them  and  establishes  their  validity. 

In  this  chapter,  then,  we  propose  to  introduce  the 
student  to  a  knowledge  of  the  elements  of  "  Science  par 
excellence "  and  to  consider  what,  if  any,  test  can  be 
found,  not  for  truths  of  this  or  that  order,  but  for  all 
truths  of  whatsoever  order. 

In  this  consideration  we  shall  have  to  make  use  of 
reasoning,  as  we  have  again  and  again  made  use  of  it, 
and  no  science  can  be  properly  followed  up  without  the 
aid  of  reasoning. 

Now  we  all  know  that  science  has  greatly  advanced 

*  See  ante,  p.  187. 


SCIENCE  367 

since  the  beginning  of  this  century.  Many  things  are 
now  known  with  absolute  certainty  which  before  it  were 
unknown.  No  one  will  probably  deny  that  science  is 
still  advancing,,  Nevertheless  such  advance  would  be 
impossible  if  we  could  not,  by  observations  and  reason- 
ings, become  so  certain  with  respect  to  some  facts,  as  to 
be  able  to  make  them  starting-points  for  fresh  observa- 
tions and  reasonings  as  to  other  facts.  It  is  impossible 
to  deny  that  we  may  repose  with  absolute  confidence  and 
entire  certainty  upon  a  variety  of  such  newly  ascertained 
facts ;  e.g.,  that  as  to  the  mode  of  reproduction  in 
ferns.* 

The  laws  of  the  reasoning  process  and  the  conditions 
of  its  validity,  have  been  explained  in  an  elementary 
manner  in  the  chapter  on  logic.  But  however  excellent 
and  admirable  our  process  of  reasoning  may  be,  the 
process  must  stop  somewhere.  For  in  order  to  prove 
anything  by  reasoning,  we  must  show  that  it  necessarily 
follows,  as  a  consequence  from  antecedent  truths,  which 
therefore  must  be  deemed  yet  more  indisputable.  But 
this  process  cannot  go  on  for  ever.  We  cannot  prove 
everything.  However  long  our  arguments  may  be,  we 
must  at  last  come  to  statements  which  have  to  be  taken 
for  granted,  otherwise  we  should  have  to  reason  for  ever, 
which  is,  in  effect,  to  affirm  that  nothing  at  all  can  ever 
be  proved.  If  we  could  not  know  some  things  without 
their  being  proved,  we  could  never  reason  validly  at  all. 
So  again  with  respect  to  the  validity  of  the  reasoning 
process  itself.  When  the  laws  of  logic  have  been  duly 
complied  with,  the  validity  of  that  process  is  a  truth 
which  we  can  see  to  be  true  by  studying  it,  and  which 
is  also  implied  in  the  fact  that  science  progresses.  If 

*  See  ante,  p.  205. 


368  ELEMENTS   OF   SCIENCE 

we  had  to  prove  the  validity  of  that  process,  such  a 
proof  would  require  a  second  proof,  that  again  would 
require  a  third,  that  third  a  fourth,  and  so  on  for  ever. 
In  other  words,  there  could  be  no  such  thing  as  proof 
at  all. 

Now  no  one  who  argues,  or  who  listens  to,  or  reads 
(with  any  serious  intention)  the  arguments  of  others, 
can,  without  stultifying  himself,  profess  to  think  that 
no  process  of  reasoning  is  valid.  If  the  truth  of  no 
mode  of  reasoning  is  certain,  if  we  cannot  draw  any 
certain  inferences  whatever,  then  all  arguments  must  be 
useless,  and  to  proffer  or  consider  them  must  be  alike 
vain.  And  not  only  must  all  reasoning  addressed  to 
others  be  thus  vain,  but  the  silent  reasonings  of  solitary 
thought  must  also  be  vain.  This  is  equivalent  to 
declaring  all  men  to  be  idiots.  But  a  man  who  honestly 
considers  all  other  men  to  be  mad,  is  generally,  and  not 
unreasonably,  deemed  to  be  somewhat  intellectually 
deficient  himself.  Thus  the  validity  of  the  process  of 
reasoning  can  but  depend  upon  its  own  evidence.  It 
depends  on  the  clear  and  manifest  evidence  it  possesses 
for  any  one  who  will  consider  it  and  who  understands 
the  meaning  of  the  idea  "  therefore " — when  plainly 
showing  how  one  truth  results  from  another — how,  e.g., 
the  mortality  of  Socrates  is  involved  in  the  fact  that 
mortality  is  common  to  the  whole  human  race. 

Thus  the  validity  of  the  process  of  reasoning  is  evident 
in  itself ;  but  the  truth  of  any  particular  inference 
depends,  and  must  depend,  upon  certain  facts  which  are 
known  to  us  independently  of  and  without  reasoning. 
We  could  not,  for  example,  conclude  that  the  fact  of 
some  animal  having  a  spinal  column,*  proved  it  to  be  a 

*  See  ante,  p.  234. 


SCIENCE  369 

"  vertebrate,"  if  we  did  not  know  that  all  vertebrate 
animals  have  a  spinal  column. 

If  we  had  no  certain  knowledge  of  any  fact,  all  our 
processes  of  reasoning  would,  as  it  were,  remained  sus- 
pended in  the  air  and  have  no  relation  with  any  real 
thing  whatever.  Now  our  knowledge  of  facts  may  vary 
greatly.  Some  men  know  an  enormously  greater  numt 
ber  of  them  than  others  do.  There  is,  however,  one  fac- 
which  everybody  knows  with  the  most  absolute  certainty, 
and  that  is  the  fact  that  he  himself  exists.*  This  know- 
ledge lies  at  the  foundation  of  our  whole  intellectual 
life.f 

The  supreme  and  absolute  certainty  which  each  of 
us  may  have  with  respect  to  this  fundamental  fact 
would  seem  to  be  indisputable ;  and  yet  there  are  some 
persons  who  dispute  it  and  affirm  that  though  we  may, 
and  do,  have  absolute  certainty  about  any  state  of  feeling 
present  at  the  moment,  no  continuous  or  substantial 
self-existence  can  certainly  be  known  to  us. 

Now,  we  have  already  affirmed  it  j  absurd  to  suppose 
our  consciousness  is  made  up  of  an  aggregate  of  states, 
and  that  we  have  no  continuous  intellectual  activity.  It 
is  now  time  to  show  how  the  delusion  that  we  cannot  be 
supremely  certain  of  our  own  continuous  existence  has 
arisen.  Our  primary,  direct  consciousness  at  any 
moment,  is  neither  a  consciousness  of  a  state  (of  a 
'*  feeling  ")  nor  of  our  continuous  existence,  but  a  per- 
ception and  consciousness  of  our  doing  something  (e.g., 
reading  this  book)  or  having  something  done  to  us  (e.g.. 
being  supported  in  a  chair).  We  have,  indeed,  all  the 
time  some  vague  perception  of  "self -existence"  and 


*  See  ante,  pp.  258  and  270.  t  See  ante,  p.  258. 

$  See  ante,  loc.  cit. 

2  A 


370  ELEMENTS   OF   SCIENCE 

some  states  of  "  feeling,"  but  what  we  perceive  primarily, 
directly,  and  immediately  is  neither  the  "  feeling "  nor 
the  "  self-existence,"  but  some  concrete  actual  doing, 
being,  or  suffering  then  and  there  experienced. 

Any  one  of  us  can,  if  he  pleases,  turn  back  his  mind 
upon  itself,  and  either  say  to  himself,  "  I  have  the 
feelings  which  accompany  reading  this  book,"  or  "it  is 
I  who  have  these  feelings."  But  neither  of  these  two 
acts  is  a  primary  act  of  the  mind.  No  one  in  beginning 
to  think,  adverts  either  to  his  "  present  feelings  "  or  to 
his  "  continuous  existence."  No  one  begins  by  per- 
ceiving his  perception  a  bit  more  than  he  begins  by 
expressly  adverting  to  the  fact  that  it  is  he  himself  who 
perceives  it.  But  to  become  aware  that  one  has  any 
definite  feeling,  is  an  act  of  reflection  which  is  at  least 
as  secondary  and  posterior  as  it  is  to  become  aware  of 
the  "  self  "  that  has  the  feeling.  Indeed  a  more  labo- 
rious effort  is  needed  to  recognise  explicitly  the  implicit 
"  feeling,"  when  we  know  we  are  doing  anything,  than 
to  bring  before  the  mind  explicitly  *  the  implicit  percep- 
tion of  our  "  persistent  existence."  Men  continually 
and  promptly  advert  to  the  fact  that  actions  and  suffer- 
ings are  their  own,  but  do  not  by  any  means  so  con- 
tinually and  promptly  advert  to  the  fact  that  the  feelings 
they  experience  are  "  existing  feelings ." 

One  of  the  greatest  and  most  fundamental  of  all 
errors,  is  the  mistake  of  supposing  we  can  know  our 
"  states  of  feeling  "  more  certainly  and  directly  than  we 
can  know  the  continuously  existing  self  which  has  those 
feelings. 

And  how  is  the  truth  of  this  perception  known  to 
us  ?  What  is  the  test  whereby  we  know  it  to  be  true  ? 

*  See  ante,  p,  255. 


SCIENCE  371 

We  know  it  to  be  true  because  we  immediately  perceive 
it.  It  is  an  evident  intuition,*  and  its  test  is  its  own 
luminous  self-evidence — its  evidence  in  and  by  itself. 
We  can  never  prove  to  ourselves  our  own  existence, 
it  is  a  self-evident  fact  which  our  intellect  directly 
perceives.  Closely  connected  therewith  is  our  power 
of  memory.f  Our  continuous  existence  is  therein 
implied,  and  the  validity  of  our  faculty  of  memory  is 
also  implied  in  every  scientific  experiment  we  perform. 
It  is  plain  that  it  would  be  impossible  for  us  to  be 
certain  about  any  careful  observation  or  any  experiment, 
if  we  could  not  place  confidence  in  our  memory  being 
able  to  vouch  for  the  fact  that  we  had  observed  certain 
phenomena  and  what  they  were. 

By  asserting  the  general  trustworthiness  of  our 
faculty  of  memory  we  do  not,  of  course,  mean  to 
deny  that  mistakes  are  often  made.  Nevertheless  we 
are  all  of  us  certain  as  to  some  past  events.  Every 
reader  of  this  book,  for  example,  is  absolutely  certain 
that  he  was  doing  something  else  before  he  began  to 
read  it. 

Memory  gives  us  as  much  certainty  concerning  some 
portions  of  the  past  as  we  can  have  with  respect  to 
some  portions  of  the  present.  If  we  could  not  trust  our 
faculty  of  memory,  all  science  would  be,  for  us,  a  mere 
dream.  But  the  veracity  of  that  faculty  is  a  self- 
evident  truth.  It  can  never  be  proved.  There  can  be 
no  such  thing  as^-oo/of  it,  because  we  cannot  argue  at 
all  unless  we  already  trust  it. 

There  is  another  important  fact  with  respect  to 
memory.  It  not  only  tells  about  our  own  past,  but 
about  various  facts  with  respect  to  other  persons  and 

*  See  ante,  p.  261.  t  See  ante,  p.  259. 


372  ELEMENTS   OF  SCIENCE 

to  things  external  to  us,  of  which  we  had  knowledge  at 
some  past  time,  as  we  shall  see  later  on.* 

But  if  we  were  provided  with  nothing  more  than 
absolutely  certain  evidence  as  to  a  number  of  facts, 
together  with  a  perception  of  the  necessary  validity  of 
the  reasoning  process,  we  could  make  no  use  of  such 
knowledge  unless  we  were  also  provided  with  some 
absolutely  certain  general  principles.  Without  them 
we  could  have  no  sure  basis  for  the  premisses  of  our 
syllogisms.  Thus,  for  example,  we  could  not  conclude 
that  Socrates  was  mortal  because  all  men  are  so,  save 
for  the  general  principle :  "  whatever  is  mortal  cannot 
at  jbhe  same  time  be  immortal." 

Such  general  principles  are  no  less  indispensable  for 
physical  science  than  for  syllogistic  reasonings. 

For  every  experiment  carefully  performed  implies  a 
conviction  on  the  part  of  him  who  performs  it  that  such 
general  principle  can  be  relied  on  with  certainty.  Let 
us  suppose  that  the  experiment  of  cutting  off  an  eft's 
leg  has  been  performed  in  order  to  see  whether  a  fresh 
leg  will  grow,  and  let  us  further  suppose  that  a  fresh  leg 
has  grown ;  this  experiment  will  have  demonstrated  that 
such  a  thing  is  possible,  because,  in  fact,  it  has  actually 
occurred.  But  that  certainty  implies  a  prior  and  much 
more  important  truth.  It  implies  the  truth  that  if  the 
eft  has  come  to  have  four  legs  once  more,  it  cannot  at 
the  very  same  time  have  still  only  three  legs.  If  we 
reflect  again  on  this  apparently  trivial  proposition,  we 
shall  see  that  it  depends  on  a  still  more  fundamental 
truth  which  our  reason  recognises — the  truth,  namely, 
that  "  nothing  can  at  the  same  time  both  be  and  not  be  "- 
which  truth  is  known  as  "  the  law  of  contradiction" 

*  See  post,  pp.  385  and  386. 


SCIENCE  373 

This  is  another  truth  which  carries  with  it  its  own 
evidence  and  is  incapable  of  proof.  That  such  is  the  case 
a  little  reflection  will  show.  We  act  upon  it  constantly 
in  daily  life  without  adverting  to  it.  We  know  that  if 
we  have  spent  all  our  money  we  can  have  none  left 
in  our  pockets,  and  we  see  plainly  that  any  man  who 
really  doubted  whether,  if  he  had  lost  one  eye,  he  might 
not  at  the  same  time  still  retain  his  original  two  eyes,  or 
who  really  doubted  whether,  if  his  legs  were  cut  off,  they 
could  not  at  the  same  time  remain  on,  would  have  a 
disordered  mind.  The  simplest  rustic  knows  that  if  his 
wages  have  been  paid  to  him,  they  are  no  longer  owing, 
and  that  if  he  has  put  his  cart-horse  in  the  stable,  it  is 
no  longer  between  the  shafts.  Yet  the  "  law  of  contra- 
diction "  is  but  the  summing-up,  in  an  abstract  formula, 
of  a  multitude  of  particular  instances  of  this  kind,  as  to 
each  one  of  which  no  doubt  is,  or  can  be,  for  a  moment 
seriously  entertained  by  any  sane  mind.  If  we  were 
really  to  doubt  about  the  law  of  contradiction  we  should 
fall  into  mere  folly.  For  if  anything  can  at  the  same 
time  both  be  and  not  be,  then  nothing  can  be  true 
without  its  being  possible  for  it  also  to  be  untrue,  and 
this  amounts  to  a  paralysis  of  the  intellect. 

But  if  we  consider  any  distant  period — such  as  the 
days  of  Julius  Caesar — or  any  distant  spot,  such  as  the 
surface  of  the  moon  or  even  the  star  Sirius,  we  can  see 
clearly  that  the  same  law  must  necessarily  also  apply  then 
and  there.  Such  a  truth  is  therefore  distinguished  as  an 
absolute,  necessary,  and  universal  truth  or  principle — 
one  applicable  to  all  times  and  all  places  whatsoever. 

Another  truth  of  a  similar  character,  but  less  uni- 
versal application,  is  an  axiom  we  before  *  noted,  namely, 

*  See  ante,  p.  34. 


374  ELEMENTS   OF   SCIENCE 

that  "  things  which  are  equal  to  the  same  thing 
are  equal  to  each  other."  This  is  an  abstract,  uni- 
versal, and  necessary  principle,  which  our  reason  can 
apprehend  to  be  such,  although  it  may  never  before 
have  been  adverted  to,  save  as  implied  in  ordinary 
facts  of  experience.  If,  for  example,  a  man  has 
found  that  two  pieces  of  wood  are  each  of  them 
equal  in  length  to  a  third  piece  of  wood  which  is 
a  yard  measure,  he  will  at  once  be  certain  that  the 
first  two  pieces  are  of  equal  length  —  namely,  each 
a  yard  long.  From  a  variety  of  instances  of  equali- 
ties of  very  different  kinds,  he  will  be  led  to  appre- 
ciate the  force  of  the  principle  just  quoted,  when  his 
attention  has  once  been  directed  to  it.  It  will  then 
be  evident  to  his  mind  that  this  equality  between 
the  equals  of  a  third  thing  must  positively  always  and 
everywhere  exist.  In  our  perception  of  the  truth  of 
this  principle — this  law — some  other  very  fundamental 
principles  are  necessarily  involved,  as  will  become 
obvious  if  we  turn  the  mind  inwards  upon  itself.  Thus 
it  is  obvious  that  this  law,  as  it  concerns  equality 
generally,  must  concern  every  kind  of  equality — equality 
not  only  between  "  quantities,"  but  between  "  qualities  " 
and  "  relations  "  also.  Two  daughters  and  a  son  of  the 
same  mother  -are  all  equally  her  children,  and  if  she 
feels  the  same  amount  of  love  for  each  girl  as  she  does 
for  her  boy,  then  the  love  felt  for  one  girl  will  be  equal 
to  that  entertained  for  the  other. 

Things  which  agree  in  quantity,  quality,  and  relation 
are  in  so  far  alike.  Yet  they  cannot  be  thought  of  as 
being  "  alike,"  unless  they  are  at  the  same  time  recog- 
nised by  the  mind  as  being  existing  things  which  are 
distinct.  Thus  in  the  above  axiom  we  have  involved 
the  ideas  " distinctness,"  "similarity,"  and  "existence," 


SCIENCE  375 

as  we  before  saw*  to  be  the  case  with  respect  to  our 
idea  of  "  number." 

This  axiom  about  equality,  though  it  can  be  illustrated 
by  any  number  of  instances,  can  never  be  proved  by 
reasoning.  It  is  a  self-evident  truth  which  reposes  on 
its  own  evidence — as  do  the  other  axioms  which  are 
characterised  as  "  evident "  in  the  second  chapter  of  this 
work. 

Self-evidence,  then,  is  our  ultimate  ground  for  assent- 
ing to  such  axioms,  as  well  as  to  necessary  principles  and 
to  the  fact  of  our  own  existence. 

We  have  already  pointed  out  f  how  universal  is  the 
desire  of  mankind  to  know  the  causes  of  circumstances 
and  events.  To  know  this  is,  as  before  said,  the  aim 
and  object  of  the  highest  form  of  science.  Particular 
sciences  may  be  devoted  to  ascertaining  that  certain 
things  are,  and  the  circumstances  of  their  being — their 
successions  and  co-existences — but  no  such  knowledge  of 
mere  phenomena  will  suffice  to  constitute  science  itself. 
Such  science  is  but  another  term  for  philosophy — the 
science  of  sciences — which  is  what  we  are  concerned  with 
in  this  chapter. 

If   we   examine   our  minds  as  to  what  our  idea  of 
"  cause  "  is  when  that  conception  is  called  forth,  we  shall    L^ 
see  that  it  stands  in  close  relation  to  our  perception  and 
idea  of  "  change." 

When  some  change  occurs,  or  when  anything  strikes 
us  as  being  a  new  thing,  we  spontaneously  look  out  for 
its  cause.  The  truth  concerning  causation,  which  our 
mind  recognises  as  being  necessary  and  self-evident,  is 
the  principle  that  "  every  new  existence  is  due  to  some 
cause" — and  this  is  quite  in  harmony  with  that  spon- 

*  See  ante,  p.  264.  t  See  ante,  p.  268. 


376  ELEMENTS   OF  SCIENCE 

taneous  habit  of  mankind  before  mentioned.  It  is  also 
a  truth,  the  self-evidence  of  which  a  little  reflection  will 
make  clear.  Thus,  a  thing  which  is  new  cannot  have 
caused  itself,  because  it  could  never  have  acted  before  it 
came  into  existence.  It  must,  therefore,  have  been 
brought  into  being  by  something  else.  But  every  change 
which  takes  place  in  a  thing  already  existing  is  also,  to 
a  certain  extent,  a  new  existence,  for  it  is  a  new  state  or 
mode  of  existence.  It  must,  therefore,  either  be  due  to 
some  antecedent  mode  of  existence  or  to  something  dis- 
tinct from  it.  Thus,  if  a  door  which  was  open  is  now 
no  longer  open,  it  must  have  been  acted  on  by  something 
else — a  current  of  air,  or  what  not.  If  a  cat  is  now 
awake  which  was  asleep,  this  must  be  due  either  to 
something  external  which  has  awakened  it,  or  to  some 
vital  action  of  its  own  frame,  which  has  aroused  it  from 
its  dormant  condition. 

Again,  all  and  every  object  made  known  to  us  by  our 
senses  is  seen  to  be  necessarily  the  product  of  some 
cause  or  causes  external  to  itself.  This  is,  of  course, 
most  manifestly  the  case  with  every  product  of  human 
art ;  but  every  stone  which  we  tread  upon,  or  every  patch 
of  sand  or  mud,  must  have  come  to  be  as  it  is  through 
the  action  of  antecedent  causes  and  conditions  which 
have  made  it  to  be  as  it  is  and  not  otherwise.  Not  only 
the  more  or  less  complex  structure  of  any  solid  body, 
but  its  size,  position,  divisibility  and  its  existence  at  the 
time  and  manner  in  which  it  does  exist,  are  all  due  to 
antecedent  actions  of  other  things  which  have  determined 
its  present  conditions  of  existence.  Even  a  portion  of 
matter,  which,  so  far  as  we  know,  is  not  made  up  of  other 
material  substances — such,  e.g.,  as  a  diamond  or  a  piece  of 
gold — demands  a  cause  for  its  relation  to  things  around  it 
and  for  its  own  size  and  internal  conditions.  The  two 


SCIENCE  377 

latter  circumstances  would  demand  a  cause  for  their  being 
such  as  they  might  happen  to  be,  even  if  such  a  body  had 
existed  eternally  in  an  eternal  universe.  Everything  then 
which  can  be  known  not  to  have  a  sufficient  cause  of  its 
existence  within  itself  must  be  due  to  some  cause  or  causes 
external  to  it.  Only  something  which  is  absolutely  simple, 
indivisible,  and  eternal,  can  escape  from  this  law  of  uni- 
versal causation.  This  perception  of  the  need  of  a  cause 
is  not  the  result  of  a  mere  negative  impotence  to  conceive 
otherwise,  but  is  a  positive  perception,  as  the  reader  may 
soon  see  for  himself  if  he  will  examine  into  his  own  mind. 
Let  him  think  of  a  stone  peculiarly  shaped,  and  then  see 
whether  his  intellect  tells  him  plainly  and  positively  that 
some  unknown  cause  or  other  must  have  determined  its 
peculiar  shape,  or  whether  his  mind  is  a  mere  blank 
with  respect  to  it. 

The  idea  of  a  cause  is  closely  connected  with  the 
conception  of  "  power "  or  "  force " — ideas  generated 
doubtless  by  our  consciousness  of  our  own  power  to 
think  or  act  and  by  our  active  exercise  of  those  powers. 
But  the  idea  of  "  power "  is  a  primary  ultimate  idea 
which  cannot  be  resolved  into  other  more  fundamental 
or  elementary  conceptions.  If  the  reader  doubts  this, 
let  him  try  whether  he  can  himself  so  resolve  it.  We 
never  of  course  see  the  "  power "  itself  which  is  thus 
exercised.  If  we  strike  a  billiard  ball  with  a  cue  we  see 
the  cue  and  the  ball,  the  blow  and  its  effects.  But  we 
can  never  see  the  influence  itself  which  the  cue  com- 
municates '}  for  it  is  invisible  as  well  as  intangible.  But 
though  our  senses  cannot  perceive  it,  our  intellect  can,  and 
there  is  one  instance,  at  least,  wherein  .the  inflow  and 
action  of  causation  is  distinctly  perceptible  to  us.  This 
is  our  perception  of  the  inflow,  of  the  influence,  of 
motives  upon  our  will.  When  we  resolve,  from  some 


378  ELEMENTS   OF   SCIENCE 

motive  to  perform  an  act,  we  are  conscious  not  merely 
of  the  existence  of  that  antecedent  state  of  things  which 
is  named  "  a  motive/'  and  of  that  consequent  which  is 
our  "  resolve,"  but  of  the  motive  also,  as  something 
impelling  us.  We  know  and  feel  that  it  is  active  and 
exerting  an  influence  upon  us ;  that  is,  emits,  as  it  were, 
a  force  stirring  our  will.  We  have  also  an  experience  of 
the  force  of  causation  when  anything  resists  our  will. 
In  the  latter  case  the  influence  is  antagonistic  to  an  act 
of  will  already  formed  ;  in  the  former  case  the  influence 
excites  towards  the  formation  of  such  an  act  of  will. 

Thus  the  "  law  of  causation  "  is  a  truth  borne  in  upon 
us  by  its  own  evidence,  not  only  spontaneously  in  each 
instance  of  it  which  comes  under  .our  notice,  but  on 
reflection  also  ;  and  the  more  we  reflect,  the  more  we  see 
the  evident  truth  and  universal  necessity  of  the  law  that 
"  every  new  existence  is  due  to  some  cause"  which  law 
is  as  certain  as  the  law  of  contradiction  itself.  For  if 
that  which  has  as  yet  no  existence  could  nevertheless  be 
a  cause,  then  it  would  no  longer  be  the  case  that  nothing 
can  at  the  same  time  both  be  and  not  be.  But  as  to  the 
nature  of  the  cause  acting  in  any  case,  our  power  of 
intellectual  intuition  tells  us  little  save  that  it  must,  in 
each  case,  be  adequate  to  produce  the  effects  to  account 
for  which  it  is  invoked.  No  child  with  a  toy  hammer 
could  level  the  great  pyramid  of  Egypt;  110  ignorant 
peasant  could,  translate  a  play  of  ^Eschylus ;  and 
no  being  devoid  of  intellect  could  perform  a  truly 
virtuous  action,  or  make  known  an  ethical  idea — for 
moral  perception  is  but  one  form  of  intellectual  activity. 
That  a  cause  must  be  adequate  in  order  that  a  given 
effect  may  be  produced  is,  an  absolute,  universal,  and 
necessary  truth,  no  less  than  is  the  law  of  causation 
itself. 


SCIENCE  379 

It  is  indeed  a  very  wonderful  thing  that  we  should  be 
able  to  know  that  any  truths  are  "  necessary "  and 
"  universal  "  ;  but  if  we  think  the  matter  all  round  and 
consider  some  of  our  other  faculties,  it  will  not  then 
appear  to  be  so  exceptionally  wonderful.  For  all  our 
knowledge  is  wonderful  when  we  consider  it  deeply.  It 
is  wonderful  that  objects  about  us,  acting  on  our  organs 
of  sense,  should  give  us  sensations  such  as  those  of 
musical  tones,  sweetness,  blueness,  or  what  not.  It  is 
wonderful,  again,  that  by  means  of  combinations  of 
sensations  actually  felt  and  others  remembered,  we 
should  be  able  to  perceive  surrounding  objects.*  It  is 
also  wonderful  that  we  should  be  able  thus  to  know  not 
only  our  present  circumstances,  but  also  something  of 
our  own  past.  In  the  same  way  it  is  wonderful  we 
perceive  that  if  a  thing  "is"  it  cannot  at  the  same  time 
"  not  be."  But  nevertheless  we  do  most  certainly  per- 
ceive that  such  is  the  case.  We  know  some  things  and 
we  know  that  we  know  them,t  and  amongst  them  we 
know  this  necessary  truth  and  also  other  necessary  truths. 
But  how  we  know  them  (or  how  we  know  anything)  is  a 
problem  to  attempt  to  solve  which  is  hopeless. 

The  mystery  of  our  power  of  intellectual  perception  is 
parallel  with  that  which  attends  our  power  of  feeling.  We 
feel  things  savoury  or  odorous,  or  brilliant  or  melodious,  as 
the  case  may  be ;  and  by  dissections  and  the  microscope  we 
may  investigate  the  structure  of  the  organs  of  sense  and 
of  the  brain.  But  how  those  anatomical  conditions  can 
give  rise  to  the  feelings  themselves,  is  a  mystery  which 
defies  our  utmost  efforts  to  penetrate.  No  one  knows  how 
knowledge  is  possible,  any  more  than  how  sensation  or 
how  life  is- possible,  or  how  solid  objects  can  have  length, 

*  See  ante,  p.  254.  t  See  ante,  p.  270. 


380  ELEMENTS   OF   SCIENCE 

breadth,  and  thickness.  But  ignorance  how  a  thing  has 
come  to  be,  does  not  in  the  least  deprive  us  of  our  cer- 
tainty of  the  fact  that  things  are — that  we  do  know  and 
feel  and  live,  and  that  dur  body  has  the  above- 
mentioned  dimensions — i.e.,  that  it  is  "  extended."  That 
we  have  a  power  of  feeling  is  evident  to  us  by  our 
senses.  That  we  exist,  and  know  universal  and  neces- 
sary truths,  is  plain  because  our  existence  and  such 
truths,  have  their  evidence  in  themselves  and  need  no 
proof — the  ground  on  which  we  believe  them  is  that 
they  are  self-evident  to  us. 

But  the  student  may  ask  whether  there  cannot  be  a 
better  criterion  of  truth  than  "  self-evidence."  Let  us 
then  see  whether  or  not  it  is  possible  to  have  a  better. 
Now,  whatever  the  supreme  and  ultimate  test  of  any 
alleged  truth  may  be,  it  must  either  reside  in  that  truth 
itself — so  making  it  luminously  self-evident — or  in 
something  else,  something  external  to  it.  But  the 
value  of  any  external  criterion  could  only  be  appreciated 
by  us  through  our  perception  of  its  cogency.  If  we 
suddenly  saw  the  law  of  contradiction  written  on  a 
cloud,  or  on  the  surface  of  the  sun,  such  a  fact 
would  not  add  to  its  cogency.  In  the  first  place,  various 
investigations  might  thereby  be  set  on  foot,  such  as  the 
sanity  of  a  witness,  or  the  probability  of  a  common 
simultaneous  hallucination,  and  so  on.  But  no  one  of 
such  investigations  could  come  to  any  conclusion  except 
the  principle  of  contradiction  were  first  absolutely 
accepted.  Thus  if  a  universal  or  necessary  truth  was 
vouched  for  by  some  external  criterion,  the  cogency  of 
which  existed  in  that  criterion  itself,  we  should  then 
only  have  self-evidence  after  all,  and  "  self-evidence"  at 
second  hand,  as  regards  the  ultimate  truth  for  which 
such  external  criterion  was  to  vouch.  If,  on  the 


SCIENCE  381 

contrary,  the  external  criterion  has  to  be  vouched  for  by 
something  again  external  to  it,  we  should  have  to  go  on 
in  that  way  for  ever,  or  else  rest  at  last  in  something 
which  was  self-evident.  It  will  be  plain,  on  reflection, 
that  nothing  external — no  common  consent  of  mankind, 
no  amount  of  testimony,  no  experimentation  or  evidence 
of  the  senses — could  ever  take  the  place  of  an  ultimate 
criterion  of  truth,  since  some  judgment  of  our  own  mind 
must  always  decide  for  us  with  respect  to  the  existence 
and  value  of  such  criteria.  Self-evidence,  then,  is  really 
the  only  possible  ultimate  test  of  truth,  and  must  be 
accepted  under  pain  of  complete  intellectual  paralysis. 
It  is  incapable  of  demonstration,  since  it  depends  on 
nothing  else.  It  is  continually  made  use  of  as  a  matter 
of  course  and  without  reflction,  and  is  relied  on  con- 
stantly by  every  one  who  reasons.  We  have  said  that 
self-evidence  must  be  accepted  under  pain  of  complete 
intellectual  paralysis,  because  if  it  be  not  accepted,  we 
are  logically  reduced  to  absolute  scepticism — that  is,  to 
utter  folly. 

It  is  necessary  that  the  student  should  recognise 
the  fact  that  we  are  all  of  us  certain  of  something. 
Although  sincere  inquiry,  and  therefore  doubt,  are  not 
only  legitimate  but  necessary  in  science,  nevertheless 
reason  shows  us  that  doubt  must  have  its  limits.  There 
is  such  a  thing  as  legitimate  certainty,  otherwise  there 
would  be  no  certain  science  of  any  kind.  But  if  there 
is  such  a  thing  as  legitimate  certainty,  then  to  doubt 
about  it  must  be  illegitimate  doubt.  But,  as  we  all 
know,  credulity  is  common  to  children  and  to  weak- 
minded,  or  ignorant,  men  and  women ;  therefore 
.extreme  scepticism  may,  at  first  sight,  seem  to  be  an 
exceptionally  intellectual  state  of  mind.  Nevertheless 
a  little  reflection  will  show  that  it  is,  in  fact,  an  excep- 


382  ELEMENTS   OF   SCIENCE 

tionally  foolish  state  of  mind  ;  for  nothing  can  be  more 
foolish  than  to  contradict  oneself;  and  that  is  what 
extreme  sceptics  are  compelled,  by  pitiless  logic,  to  do. 
We  have  met  with  a  notable  example  of  this  folly  in  the 
case  of  Pyrrho*  and  his  disciples  the  Pyrrhonists,  who 
refused  even  to  affirm  the  truth  of  their  own  system. 
If  any  one  should  venture  to  say  "  Nothing  is  cer- 
tain," he  would  necessarily  contradict  himself,  for  he 
would  thereby,  in  the  very  same  breath  say,  or  at  least 
imply,  that  "  something  is  certain,"  since  he  implies  that 
we  may  be  certain  nothing  is  certain.  He  says,  or 
implies,  therefore,  something  which,  if  true,  absolutely 
contradicts  what  he  has  declared  to  be  true.  But  a 
man  who  affirms  what  the  system  he  professes  to  adopt 
forbids  him  to  affirm,  and  who  declares  that  he  believes 
what  he  also  declares  to  be  unbelievable,  can  hardly 
complain  if  he  is  called  foolish.  If  he  denies  that  he 
affirms  anything,  or  even  that  he  doubts  about  every- 
thing, then,  since  he  affirms  nothing,  we  may  disregard  his 
avowed  folly,  and  the  utter  impotence  he  confesses  to. 

Let  us  see  a  little  further  how  self -refuting  sceptical 
modes  of  thought  are.  Suppose  a  man  were  to  say :  "I 
cannot  be  sure  of  anything,  because  I  cannot  be  certain 
that  my  faculties  are  not  always  fallacious,"  or,  "I 
cannot  be  sure  of  anything,  because,  for  all  I  know,  I 
may  be  the  plaything  of  a  demon  who  amuses  himself 
by  constantly  deceiving  me  " — in  both  these  cases  such  a 
man  would  simply  contradict  himself.  Jfor  how  can  he 
know  that  " constantly  fallacious  faculties,"  or,  "a 
demon  deceiving  in  all  things,"  will  necessarily  deprive 
him  of  certainty  ?  Obviously  he  can  only  know  this, 
because  he  sees  the  necessary  truth  :  "it  is 


*  See  ante,  p.  329. 


SCIENCE  383 

arrive  at  conclusions  which  are  certain,  by  means  of  what 
is  uncertain  or  false."  But  if  he  knows  that  truth — if 
he  is  certain  of  that  universal  principle — he  must  know 
that  his  faculties  are  not  always  fallacious,  and  that  his 
demon  is  impotent  to  deceive  him  in  everything — since 
he  can  apprehend  the  certainty  of  the  necessary  truth 
last  stated.  Universal  doubt,  then,  is  simply  an  absur- 
dity. It  is  scepticism  run  mad,  and  no  system  can  be 
true,  and  no  reasoning  can  be  valid,  of  which  the 
inevitable  result  is  scepticism  of  such  a  nature. 

Let  us  now  see  what  would  be  the  consequences  of 
uncertainty  as  to  the  validity  of  the  reasoning  process 
and  our  mental  faculties  generally,  of  memory,  of  our 
knowledge  of  our  own  existence,  or  of  universal  necessary 
principles,  or  of  the  law  of  contradiction. 

As  to  reasoning,*  and  the  trustworthiness  of  our 
mental  faculties  generally,  if  any  man  is  convinced  that 
thoughts  are  worthless  tools,  he  can  only  have  arrived  at 
that  conclusion  by  using  the  very  tools  he  professes  to 
consider  worthless.  What,  then,  ought  his  conclusions 
to  be  worth  even  in  his  own  eyes  ?  It  is  simply  im- 
possible by  reason  to  get  behind  or  beyond  conscious 
thought,  and  our  thoughts  are,  and  must  be,  our  only 
means  of  investigating  fundamental  problems. f  If  a 
man  professes  to  affirm  that  his  faculties  are  untrust- 
worthy, we  of  course  are  thereby  debarred  from  bringing 
home  conviction  to  his  mind.  But  it  is  no  less  im- 
possible for  him  to  defend  his  position.  Once  let  him 
attempt  sincerely  to  do  so,  and  he  thereby  plainly  shows 
that  he  really  has  confidence  in  reason  and  in  language, 
however  much  he  may  verbally  deny  that  lie  has  it.  It 


*  For  the  consequences  of  scepticism  as  to  this,  see  pp.  368 
and  369.  t  See  ante,  p.  270. 


3§4  ELEMENTS   OF   SCIENCE 

is  clear  that  we  all  do  know  and  are  certain  about  some- 
thing, if  only  that  we  are  inquiring  about  the  certainty 
of  knowledge.  Utter  folly,  then,  logically  results  from 
doubt  as  to  the  validity  of  reasoning. 

Evidently,  mental  paralysis  must  also  result  from  any 
real  doubt  about  our  own  existence,  and  our  perception 
of  this  existence  involves  the  validity  of  our  faculty  of 
memory,  which  is  implied  in  this  way  as  well  as  in  every 
scientific  experiment  we  perform.  For  we  cannot  obvi- 
ously have  a  reflex  perception*  either  of  our  feelings 
or  our  self-existence,  without  trusting  our  memory  as  to 
the  past. 

Now  there  are  two  technical  terms  with  which  the 
student  who  desires  to  be  introduced  to  the  elements  of 
science  must  make  himself  familiar. 

They  may  be  represented  to  a  certain  extent  by  the 
two  familiar  words  "facts "  and  "feelings"  The  two 
technical  terms  which  correspond  with  them  respectively 
are  :  (i)  things  which  are  objective,  and  (2)  things  which 
are  subjective. 

Every  "  feeling  "  or  "  state  of  consciousness  "  present 
to  the  mind  of  whoever  is  the  subject  of  it,  is  spoken  of 
as  being  "  subjective,"  and  the  whole  of  such  experience, 
taken  together,  constitutes  the  sphere  of  "  subjectivity." 

On  the  contrary,  everything  whatever  which  exists 
externally  to  our  present  "  consciousness  "  or  "  feelings," 
is  spoken  of  as  being  "  objective,"  and  all  that  is  thus 
external  to  the  mind  is  the  region  of  objectivity ;  it  is 
the  region  of  facts  as  considered  apart  from  feelings. 
But  the  reader  must  understand  that  the  feelings  of  one 
man  are  "  objective  facts  "  to  any  other  man  ;  only  a  man's 
own  present  thoughts  and  feelings  are  to  him  "  subjective." 

*  See  ante,  p,  259. 


SCIENCE  385 

Now  memory  informs  us  with  absolute  certainty  as  to 
some  events  of  our  own  past  history.  But  such  events  are 
beyond  our  present  experience,  therefore  they  have  a 
truth  which  extends  back  beyond  any  present  feeling  we 
have.  They  are  realities  existing  in  addition  to  our 
present  feelings,  and  they  are  therefore  "  objective. " 
Thus  memory,  insomuch  as  it  reveals  to  us  part  of  our 
own  past,  reveals  to  us  what  is  "objective,"  and  so 
actually  introduces  us  into  the  realm  of  objectivity,  shows 
us  more  or  less  of  "  objective  "  truth,  and  carries  us  into 
a  real  world  which  is  beyond  the  range  of  our  present 
feelings.  This  power  which  memory  has  of  thus  lifting 
us,  as  it  were,  out  of  our  present  selves  and  showing  us 
such  facts,  is  certainly  a  very  wonderful  power ;  and  yet 
its  existence  must  be  admitted,  at  the  price  of  otherwise 
falling  into  a  most  absurd  and  idiotic  scepticism  which 
would  deprive  us  of  all  power,  not  only  of  reasoning 
with  others,  but  of  having  any  rational  perceptions 
ourselves.  The  moment  lasts  but  a  moment.  If  we 
could  not  know  with  certainty  more  than  the  passing 
moment,  we  could  not  really  know  even  that.  We  could 
know  nothing. 

As  to  necessary  truths,  if  we  were  to  doubt  about  the 
"law  of  contradiction,"  we  could  again  be  certain  of 
nothing.  If  we  would  rise  from  such  intellectual 
paralysis  we  must  accept  that  dictum  as  it  presents  itself 
to  our  minds ;  and  that  dictum  declares  that  nothing  can 
both  be  and  not  be ;  e.g.,  that  no  creature,  anywhere  and 
anywhen,  can,  at  the  same  time,  be  both  bisected  and 
entire.  As  to  the  "  law  of  causation,"  its  doubt  or 
denial  would  annihilate  physical  science,  and  also,  as 
we  have  seen,*  would  involve  a  denial  of  the  law  of 

*  See  ante,  p.  379. 

2  B 


386  ELEMENTS   OF   SCIENCE 

contradiction,  and  so  reduce  us  to  the  idiocy  of  absolute 
intellectual  paralysis. 

But  we  all  know  that  we  have  a  body  as  well  as  a 
mind,  and  that  the  body  has  the  dimensions  before  men- 
tioned,* i.e  ,  is  "  extended."  Similarly  we  perceive  that 
other  bodies  are  extended  also,  and  we  do  this  not  by 
any  process  of  inference  f  from  sensations  arising  in  us 
through  the  influence  of  objects  about  us,  but  by  a  direct 
intuition  which  such  sensations  occasion.  It  is  not  a 
synthesis  of  such  sensations  ;  for  they  continue  to  exist 
.separately  and  can  be  recognised  by  the  mind  as  doing  so 
and  standing  as  it  were  beside  the  direct  perception  they 
have  occasioned  which  persists  during  the  recognition  of 
the  sensations  which  have  occasioned  it.  No  mistake 
can  be  greater  than  that  of  thinking  a  perception  is  made 
up  of  the  feelings  which  minister  to  it.  Two  marbles 
are  objectively  two,  and  can  be  so  perceived,  whatever  the 
subjective  impressions  which  have  occasioned  them.  As 
we  lately  said,  our  memory  has  the  power  of  lifting  out 
of  mere  subjectivism  into  a  certain  knowledge  of  objective 
truth.  Doubtless  our  faculties  do  not  enable  us  to  fully 
understand  or  know  all  the  properties  of  bodies.  It  may 
well  be  that  we  might  have  additional  senses  which  would 
reveal  more  of  such  properties— as  we  might  have  a 
sense  which  would  enable  us  to  perceive  the  magnetic 
•qualities  of  bodies.  But  our  perceptions,  though  inade- 
quate to  tell  us  all  we  might  know,  are  not  mendacious. 
We  know  that  bodies  exist  objectively,  and  many  of  their 
objective  conditions  of  existence,  some  of  which  give 
rise  to  two  very  notable  abstract  ideas,  namely,  those  of 
.space  and  time. 

*  See  ante,  p.  381.  t  See  ante,  p.  255. 


SCIENCE  387 

All  corporeal  bodies  are  commonly  spoken  of  as 
occupying  some  "  portion  of  space,"  but  we  have  no 
evidence  of  the  existence  of  any  such  thing  as  "  space? 
and  the  conception  of  ether*  everywhere  diffused,  does 
away  with  all  need  for  calling  up  such  a  phantom  of  the 
imagination.  Things  are  "  extended,"  but  there  is  no 
such  thing  as  "  extension,"  and  when  we  think  of  the 
latter,  we  always  vaguely  imagine  some  extended  body, 
When  we  speak  of  "  space,"  however,  we  do  not  mentally 
refer  to  any  extended  body ;  what  we  mean  is  the  quality 
of  extension,  as  completely  abstracted  from  all  bodies 
whatever  and  thought  of  purely  by  itself.  "  Extension  " 
has,  of  course,  no  existence  in  itself  as  extension ;  though 
it  is  real  and  objective  as  a  quality  of  real  extended 
objects.  "  Space "  is  altogether  ideal,  an  abstraction 
from  abstractions,  and  when  we  speak  of  bodies  "  occu- 
pying space,"  we  really  refer  to  the  exclusion  of  one 
extended  body  by  another.  "  Space,"  then,  though 
there  is  no  such  thing  as  space,  is  a  true  idea  which 
signifies  the  extension  of  all  extended  things  taken 
together  and  considered  abstractedly.  This  truth  does- 
away  with  and  explains  the  problem  which  has  puzzled 
so  many — is  space  endless  or  not?  For  it  is  not 
evident  that  there  must  be  an  endless  succession  of 
extended  bodies  in  all  directions,  while  space  cannot 
go  beyond  extended  bodies,  since  it  is  nothing  but  the 
abstract  idea  of  their  common  extension  and  mutual 
exclusion.  That  we  cannot  imagine  a  boundary  to 
space  is  simply  due  to  our  having  had  no  such  expe- 
rience, for  we  can  never  imagine  anything  of  which 
we  have  had  no  sort  of  experience;  and  we  have 

*  See  ante,  p.  93. 


388  ELEMENTS   OF   SCIENCE 

had  no  experience  of  any  extended  body  with  nothing 
beyond  it. 

Similarly,  "  time  "  is  an  abstraction  from  abstractions. 
Things,  in  our  experience,  really  endure  more  or  less 
and  succeed  one  another.  But  the  ideas  "  endurance  " 
and  "  succession,"  are  nothing  but  abstractions  in  them- 
selves, though  they  are  real  and  objective  as  qualities  of 
enduring  and  succeeding  things.  "  Time  "  is  altogether 
ideal ;  and  when  we  speak  of  events  as  occurring  in  time, 
it  is  a  mere  mode  of  speaking  which  denotes  the  endurance 
and  succession  of  succeeding  things  and  the  exclusion  of 
one  succeeding  thing  by  another,  together  with  the 
duration  of  the  mutual  exclusion  of  all  succeeding  things. 
In  the  absence  then  of  any  succession  there  could  be  no 
« time." 

But  the  things  which  succeed  and  which  are  extended, 
we  can,  and  do,  know  more  or  less  perfectly,  as  they 
are  in  themselves,  and  apart  from  any  distortion  of 
truth  due  to  the  action  of  our  own  faculties.  Thus,  as 
beforesaid,  two  marbles  are  two,  and  would  be  two 
(we  see  and  know)  were  every  human  mind  annihilated, 
and  would  still  be  extended  and  rounded  in  shape 
were  there  no  living  creature  on  the  surface  of  our 
planet. 

We  saw  in  the  last  chapter  that  the  Greek  philo- 
sophers, Arcesilaus  and  Carneades,*  taught  that  we  could 
know  nothing  but  appearances,  and  that  all  our  know- 
ledge was  merely  relative.  Unlike  Pyrrho,  they  did  not 
hesitate  to  affirm  the  truth  of  their  systems  of  philosophy. 
The  same  system  is  professed  by  some  amongst  us  to-day, 
and  may  be  thus  stated  : 

i .  All  our  knowledge  is  merely  relative. 
*  S2e  ante,  p.  330. 


SCIENCE  389 

2.  We    can    know    nothing    but    appearances,    i.e., 
phenomena. 

3.  We  cannot  emerge  from  the  sphere  of  objectivity 
and  attain  any  knowledge  of  things  objective. 

Now  of  course  anything  which  is  "known  to  us" 
cannot  at  the  same  time  be  " unknown  to  us"  and  so 
far  our  knowledge  may  be  said  to  affect  the  thing  we 
know.  But  this  is  trivial.  Our  "  knowing  "  or  "  not 
knowing'"'  any  object,  is — apart  from  some  act  which 
may  be  the  result  of  such  knowledge — a  mere  accident 
of  that  object's  existence,  which  is  not  otherwise  affected 
thereby. 

But  indeed  the  system  of  the  "relativity  of  know- 
ledge" really  refutes  itself.  For  every  system  of 
knowledge  must  start  with  the  assumption,  implied  or 
expressed,  that  something  is  true,  or  known  so  to  be. 
By  the  teachers  of  the  doctrine  of  the  "relativity  of 
knowledge,"  it  is  taught  that  the  doctrine  of  the  rela- 
tivity of  knowledge  is  thus  true.  But  if  we  cannot 
know  that  anything  corresponds  with  external  reality,  if 
nothing  we  can  assert  has  more  than  a  relative  and 
phenomenal  value,  then  this  character  must  also  apper- 
tain to  the  doctrine  of  the  "  relativity  of  knowledge " 
itself.  Either,  then,  this  system  of  philosophy  is  itself _ 
merely  relative  and  phenomenal,  and  so  cannot  be  known 
to  be  true,  or  else  it  is  absolutely  true,  and  can  be  known 
so  to  be.  But  it  must  be  merely  relative  and  pheno- 
menal, if  everything  known  by  man  is  such.  Its  value 
then  can  be  only  relative  and  phenomenal,  therefore  it 
cannot  be  known  to  correspond  with  external  reality, 
and  cannot  be  asserted  to  be  true.  If  anybody  asserts 
that  we  can  know  the  system  of  the  relativity  of  know- 
ledge to  be  true,  he  thereby  asserts  that  it  is  false  to  say 
that  all  our  knowledge  is  only  relative.  In  asserting 


390  ELEMENTS   OF  SCIENCE 

that  we  can  know  the  system  of  the  relativity  of  know- 
ledge to  be  true,  he  who  so  asserts  proclaims  that  some 
of  our  knowledge  must  be  absolute ;  but  this  upsets  the 
foundation  of  his  whole  system. 

Any  one  who  upholds  such  a  system  as  this,  may  be 
compared  to  a  man  seated  high  up  on  the  branch  of  a 
tree,  which  he  is  engaged  in  sawing  across  where  it 
springs  from  the  tree's  trunk.  The  position  and  occupa- 
tion of  such  a  man  can  hardly  be  considered  as  evidence 
of  wisdom  on  his  part. 

The  simple  but  fundamental  truths  to  which  attention 
has  been  called  in  this  chapter,  are  really  present  in  the 
mind  of  every  rational  man,  though  they  may  be  un- 
observed or  very  imperfectly  apprehended  by  him.  They 
have  most  important  and  far-reaching  consequences, 
and  merit  the  attention  of  every  one  who  desires  to 
be  able  to  give  a  reasonable  account  of  the  convic- 
tions of  his  own  mind.  They  are  truths  which  are 
latent  in,  and  so  necessary  for  the  validity  of,  every 
branch  of  science,  that  any  real  doubt  about  them 
would  make  not  only  experiment,  but  even  observation, 
logically  impossible. 

The  truths  here  put  forward  are,  as  before  said,  truths 
of  science  par  excellence,  as  distinguished  from  its  various 
branches  with  which  we  have  been  concerned  in  previous 
chapters.  They  are  truths  of  philosophy,  and  as  tran- 
scending evei^branch  of  "physics"  constitute  what  we 
call  "  metaphysics. 

But  the  student  who^i^.  perusing  this  chapter,  meets 
with  ideas  and  reasoning  with  which  he  was  before  un- 
familiar, must  not  imagine  that  by  mastering  them  he 
can  acquire  a  knowledge  of  metaphysical  truth  or  philo- 
sophy. Some  fragments  of  that  truth  he  can  thus 


SCIENCE  391 

acquire,  but  he  must  bear  in  mind  that  in  this  chapter, 
as  in  the  preceding  chapters,  we  have  but  given  him  an 
introduction  to  the  elements  of  the  science  therein 
treated  of. 

A  philosophical  foundation  is  absolutely  necessary, 
however,  to  establish  the  validity  of  all  sciences — that  is, 
fundamental,  or  metaphysical,  science  must  support  and 
justify  all  its  subordinate  branches.  By  various  com- 
binations of  the  different  lines  of  inquiry — different  kinds 
of  study — which  we  have  considered  in  this  book,  each 
distinct  science  is  constituted. 

Thus  (the  co-operation  of  philosophy  being  in  each 
case  understood)  by  a  combination  of  mathematics  with 
the  sciences  which  regard  the  stability  and  movements 
of  bodies  and  the  action  of  the  various  physical  energies, 
we  have  the  vast  science  of  Physics.  By  the  study  of 
the  laws  of  life,  taken  in  conjunction  with  the  lines  of 
inquiry  included  under  physics,  we  have  Biology,  with  its 
subordinate  group  of  sciences  such  as  physiology,  anat- 
omy, &c.  By  the  aid  of  psychology,  taken  with  biology 
as  applied  to  man,  we  have  the  special  science  of  man- 
kind or  Anthropology,  one  department  of  which  is  logic. 
By  the  application  of  facts  drawn  from  anthropology, 
especially  as  regards  moral  intuitions  and  moral  rela- 
tions, we  have  the  science  of  right  and  wrong,  that  is 
Ethics.  By  a  study  of  ethics  and  certain  departments  of 
anthropology,  taken  in  conjunction  with  the  law  of 
•causation  and  with  history,  we  have  Theology.  Lastly, 
from  anthropology,  and  the  last-mentioned  science, 
together  with  ethics,  we  may  attain  the  science  of,  and 
rules  for,  the  reasonable  regulation  of  men  in  communi- 
ties, so  as  to  produce  the  greatest  good,  namely,  the 
science  and  the  art  of  Politics. 


392  ELEMENTS    OF   SCIENCE 

The  object  of  this  little  book  is  to  promote  the 
cultivation  of  such  organised  knowledge.  Its  aim  has 
been  so  to  guide  the  student's  first  steps  that,  by  a 
simultaneous  introduction  to  the  various  sciences,  he 
may  come  to  apprehend  the  close  connection  and 
reciprocal  relations  which  exist  between  them  all.  The 
author's  hope  is  thus  to  stimulate  desire  for  the  pursuit 
of  every  one  of  those  sciences  the  due  cultivation  of 
which  is  of  such  supreme  importance  to  the  welfare 
of  mankind. 


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London  and  Edinburgh 


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